Patent Publication Number: US-11044971-B2

Title: Faceted gemstone for focal point illumination and method of making faceted gemstone

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 62/694,307, filed on Jul. 5, 2018, which is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Flat faceted gemstones have limited refraction and reflection with little further improvement of a gem&#39;s beauty. A trade-off between color, brightness, and style of cut in the flat faceted gem is a juggling act. Many “round brilliant” gemstones are disappointing, for example, in the lack and saturation of color from all its 58 flat facets. The gemstone industry has failed to provide beautiful alternatives to flat-faceted gemstones, such as the round brilliant gemstone. 
     As used in the disclosure that follows and as is well known in the art, the focal length of a ball lens (f) is defined by the index of refraction (n) times the diameter (D) of the ball lens divided by four times (n−1), which can be generally expressed algebraically as: 
     
       
         
           
             
               f 
               = 
               
                 
                   n 
                   ⁢ 
                   D 
                 
                 
                   4 
                   ⁢ 
                   
                     ( 
                     
                       n 
                       - 
                       1 
                     
                     ) 
                   
                 
               
             
             . 
           
         
       
     
     SUMMARY 
     One embodiment provides a gemstone, including: a top portion having a spheroidal surface, the spheroidal surface acting as a refractive surface for light incident on the top portion of the gemstone and focal point lens originator; and a bottom portion shaped as a cone, the cone acting as a light axis to form a focal point on a reflective surface at a base of the gemstone. 
     Another embodiment provides a jewelry piece, including: a first gemstone and a second gemstone. The first gemstone comprises: a top portion having a spheroidal surface, the spheroidal surface of the first gemstone acting as a refractive surface for light incident on the top portion of the first gemstone and focal point lens originator; and a bottom portion shaped as a cone, the cone acting as a light axis of the first gemstone to form a focal point on a reflective surface at a base of the first gemstone; wherein at least some of the light that is reflected by the base of the first gemstone enters the second gemstone to illuminate the second gemstone. 
     Yet another embodiment provides a method for faceting a gemstone comprising: shaping a top portion of the gemstone to have a spheroidal surface, the spheroidal surface acting as a refractive surface for light incident on the top portion of the gemstone and focal point lens originator; and shaping a bottom portion of the gemstone as a cone, the cone acting as a light axis to form a focal point on a reflective surface at a base of the gemstone. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a cross-section of round brilliant cut gemstone of the prior art. 
         FIGS. 2A-2B  illustrate a cross-section of a focal point brilliant spheroidal faceted gemstone according to various embodiments of the disclosure. 
         FIGS. 3A-3C  illustrate views of a focal point brilliant spheroidal gemstone according to an embodiment of the disclosure. 
         FIGS. 4A-4C  illustrate views of a spheroidal gemstone according to an embodiment of the disclosure. 
         FIG. 5  is an example of a faceted spheroidal gemstone according to the embodiment of  FIG. 3A . 
         FIGS. 6A-6C  illustrate views of a smooth dome hemispheric gem with slightly concave sides according to an embodiment of the disclosure. 
         FIGS. 7A-7C  illustrate views of a gem with a spheroid top according to an embodiment of the disclosure. 
         FIGS. 8A-8B  illustrate views of a linearly arranged row of gem spheroids according to an embodiment of the disclosure. 
         FIGS. 9A-9B  illustrate views of circularly arranged gem spheroids according to an embodiment of the disclosure. 
         FIGS. 10A-10C  illustrate views of a gem according to an embodiment of the disclosure. 
         FIGS. 11A-11D  illustrate views of a gem according to an embodiment of the disclosure. 
         FIGS. 12A-12C  illustrate views of an oval spheroidal gem according to an embodiment of the disclosure. 
         FIGS. 13A-13C  illustrate views of a double gem according to an embodiment of the disclosure. 
         FIGS. 14A-14D  illustrate views of a gem according to an embodiment of the disclosure. 
         FIGS. 15A-15C  illustrate views of a spheroidal gem with beveled bands according to an embodiment of the disclosure. 
         FIGS. 16A-16C  illustrate views of an oval spheroidal gem with beveled cuts according to an embodiment of the disclosure. 
         FIGS. 17A-17C  illustrate views of a gem according to an embodiment of the disclosure. 
         FIGS. 18A-18D  illustrate views of a gem according to an embodiment of the disclosure. 
         FIGS. 19A-19C  illustrate views of a gem according to an embodiment of the disclosure. 
         FIGS. 20A-20C  illustrate views of a gem with a bulbous top according to an embodiment of the disclosure. 
         FIGS. 21A-31C  illustrate examples of faceted gemstones, according to various embodiments. 
         FIG. 32  illustrates a cross-section of a focal point brilliant spheroidal faceted gemstone according to yet another embodiment of the disclosure. 
         FIGS. 33A-33C  illustrate an examples of the spheroidal faceted gemstone of  FIG. 32 , according to one embodiment. 
         FIG. 34  is a method for faceting a gemstone, according to one embodiment. 
         FIGS. 35A-35C  illustrate views of an arrangement of two spheroidal faceted gemstones according to an embodiment of the disclosure. 
         FIGS. 36A-36C  illustrate views of another arrangement of two spheroidal faceted gemstones according to an embodiment of the disclosure. 
         FIGS. 37A-37C  illustrate views of yet another arrangement of two spheroidal faceted gemstones according to an embodiment of the disclosure. 
         FIGS. 38A-38C  illustrate views of an arrangement of a spheroidal faceted gemstone and a heart-shaped gemstone according to an embodiment of the disclosure. 
         FIGS. 39A-39C  illustrate views of an arrangement of three spheroidal faceted gemstones according to an embodiment of the disclosure. 
         FIGS. 40A-40D  illustrate various examples of multiple spheroidal faceted gemstones in a pendant according to various embodiments of the disclosure. 
         FIGS. 41A-41C  illustrate views of of multiple spheroidal faceted gemstones in a pendent or broach according to one embodiment of the disclosure. 
         FIGS. 42A-42D  illustrate various examples of multiple spheroidal faceted gemstones in a pendant or broach according to various embodiments of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Light waves can be described as a wave phenomenon having a velocity, frequency and wavelength. Frequency (f), velocity (V) and wavelength (λ) can be related by the equation, f=V/λ. Frequency of light remains constant regardless of the material that the light travels through; hence, as velocity of light changes through a medium, wavelength changes to hold the relationship. Refraction occurs as a result of velocity changes of light traveling from one medium to another. Sunlight, often referred to as white light, includes different light wavelengths, so as a ray of sunlight hits a glass prism, the glass prism reduces the velocity of the ray of sunlight. Since sunlight is composed of multiple wavelengths, the speed of each wavelength is reduced differently resulting in separation of sunlight into separate colored rays of different wavelengths to comprise the natural visible spectrum that we see. Intensity of the brightness of the incident ray of sunlight is proportional to the square of the amplitude of the ray of sunlight. 
     The velocity of light depends on the nature of the material that the light travels through and the wavelength of the light. Light has a maximum possible speed of 3×10 8  m/sec in a vacuum and is slowed down in any other medium. The slowdown is a result of interaction between the electric vector of the light and the electronic environment around each atom in the medium, especially electrons of the atoms. In some implementations, closely packed carbon atoms in diamond cut light speed by 2.42 times. 
     Light bends when passing from one medium to another at an angle other than perpendicular to the boundary between the two media. The “index of refraction” or “refractive index” (n) is a measure of how effective a material is in slowing light, or bending light coming from a vacuum. The refractive index n=(V v )/V, where V v  is the velocity of light in a vacuum and V is the velocity of light in the material. The refractive index of a vacuum is 1.0 and for all other materials greater than 1.0. In some implementations, velocity of light in air is almost the same as the velocity in a vacuum and can be approximated as 1.0. In general, light is refracted towards the normal to the boundary on entering a material with higher refractive index and is refracted away from the normal on entering a material with lower refractive index. 
     Over 450 years of gemstone enhancement has resulted in spectacular gemstones with numerous flat facets that take advantage of wave properties of visible light. A compromise between color, brightness, and shape of gemstone has given, as an example, the “round brilliant” gemstone, one of many styles of cuts of gemstones. Although variations in quality still occur with the final polished result, a sparkling gem usually ensues, giving brightness and many tones of color of the natural visible spectrum from the 58 flat, mathematically precise, sparkling facets of the round brilliant cut gemstone. Present state of the art of faceting does not allow sunlight to be focused in the gemstone. Colors reflect off the gemstone&#39;s multiple flat facets to the eye of the viewer. 
     As described in greater detail herein, spheroidal sculpturing or faceting affects the light properties, and therefore beauty, of a gemstone in several ways. Spheroidal faceting can affect the number and saturation of colors present, increasing brightness in the gemstone, brilliance, and sparkle or scintillation on rotation. In some embodiments, combining gems in pairs dazzles both gems. 
     Described in this disclosure are a gemstone and methods of faceting gemstones with spheroidal gem optics that focus light rays inside or near the bottom of the gemstone and reflect colors throughout the gemstone to an outside observer. Also described in this disclosure are enhanced surface structures (e.g., external shapes and other surface features) that cause refraction and reflection in gemstones. Also described in this disclosure are methods of enhancing refraction and reflection in gemstones. Also described in this disclosure are methods to capture and reflect focused colorful rays and brightness for an outside observer, such that the rays of light exhibit a lessor amount of leakage, following a shortest, most direct path while traveling into, through and exiting the gemstone to the outside observer. 
     According to various embodiments, using the laws of refraction and reflection applied to spheroidal shapes, gemstones and gem materials can be faceted to exhibit more saturated and numerous, longer-lasting spectral colors, intense illumination, greater brilliance, and enhanced scintillation. Additionally, using gem materials with relatively higher refractive indices can achieve even greater results. For example, diamond has a refractive index of 2.417 and a dispersion of 0.044. In some embodiments, faceted spheroidal diamonds have more numerous saturated colors than faceted diamonds of the present state of the art. 
       FIG. 1  illustrates a cross-section of a round brilliant cut gemstone  100  of the prior art. The round brilliant cut gemstone  100  may be a diamond with refractive index of 2.417. The crossection shown in  FIG. 1  illustrates incoming light rays  102 A,  102 B incident on the gemstone  100 . Light ray  102 A is refracted as it enters the gemstone  100  at location  104 A. In the example shown, light ray  102 B is perpendicular to a top surface  130  (i.e., table) of the gemstone  100 , and is thus not refracted when it intersects the gemstone at location  104 B. Light rays originating or continuing from locations  104 A,  104 B are reflected at locations  106 A,  106 B, respectively, on an oppostise (i.e., bottom) side of the gemstone  100  from the side (i.e., top) of the incident light rays  102 A,  102 B. After the light ray reflects from location  106 A, the light ray intersects the gemstone  100  again at location  108 A, where the light ray is refracted and exits the gemstone  100  as light ray  120 A. After the light ray reflects from location  106 B, the light ray intersects the gemstone  100  again at location  108 B, where the light ray is reflected once more, and intersects the gemstone  100  a third time at location  110 B, and then refracts on exiting the gemstone  100  as light ray  120 B. It should be understood that at each interaction of the light rays with a boundary of the gemstone, some light may be reflected and some light may be refracted based on the Fresnel equations. For purposes of illustration, the primary interaction (i.e., reflection or refraction) is illustrated in  FIG. 1  for each intersection with the gemstone boundary. 
     In  FIG. 1 , some incident light (e.g., sunlight) refracts on entering the gemstone  100  an an angle relative to the surface normal of the facet that the light ray intersects. Angled facets of the crown (i.e., top) of the gemstone  100  refract the incident light into colored rays. Incident light that enters the table of the gemstone  100  perpendicular to the table is not refracted (e.g., incident light ray  102 B). Colored rays and unrefracted sunlight then reflect off two pavilion facets and refract a second time on exiting the gemstone  100 . Unrefracted incident sunlight may refract upon exiting the gemstone  100  into colored rays. Refracted colored rays leave the crown and reflect off adjacent facets to the observer. The tone of colors of the return light may vary, with many flat facets absent of color at any position. Other flat facets on the crown of the gemstone overpower with brilliant color. However, some incident light will leak out the bottom of the gemstone  100  and not return to the viewer, such as light ray  120 A. Such light leakage may result in a darker area in the gemstone and less “sparkle.” 
     In comparision,  FIG. 2A  illustrates a cross-section of a focal point brilliant spheroidal faceted gemstone  200  for self-illumination according to an embodiment of the disclosure. In one embodiment, the spheroidal faceted gemstone  200  of  FIG. 2A  can be a zircon with refractive index of 2.00. In other embodiments, the gemstone  200  may be of any transparent or semitransparent material, including diamond. The cross-section of of the gemstone  200  shows that the gemstone  200  has a spheroidal surface  202  at the top  206  (crown) of the gemstone  200  that refracts incoming light rays A, B to a focal point  204  at the bottom  208  of the gemstone  200  (culet). At the bottom  208  of the gemstone  200 , colored rays and sunlight at the focal point  204  are reflected back towards the spheroidal surface  202  and then out of the gemstone  200  as colored light rays  210 A,  210 B. In one embodiment, the bottom  208  of the gemstone is a sharp point, as shown in  FIG. 2A . In another embodiment, the bottom  208  of the gemstone is a small flat facet (culet). In another embodiment, the bottom  208  of the gemstone approximates a slightly rounded surface with a series of small flat facets. In other embodiments, the bottom  208  of the gemstone can have any shape. 
     The spheroidal gemstone  200  of  FIG. 2A  causes incident light that enters the gemstone parallel to a light axis  290  to focus to a focal point or area inside the gemstone  200 , on the bottom surface of the gemstone  200 , or just outside the bottom surface the gemstone  200  (e.g., a mother-daughter pairing, as discussed below), depending on depth of the gemstone and the refractive index of the gemstone. It should be understood that in various implementations, the focal “point” can be a singular point or an area. 
     The shape of the gemstone  200  can also vary based on the refractive index of the gem material. For example, the shape of the gem may be cut to be similar to that of an American football shape, for example, i.e., greater than spheroidal. The design of the gem can be configured such that the focal point  204  is within the gem to reflect from facets or basins at the bottom of the gem. According to various embodiments, the spheroidal faceted gemstone can be designed with numerous reflective facets at the bottom of the gem that show brilliant, saturated colors of the visible light spectrum, from red to violet, in any position of the gemstone. In some embodiments, the spheroidal surface  202  is rounded, e.g., polished rounded surface. The polished rounded surface may have a mirror-like finish, in some implementations. In other embodiments, the spheroidal surface is formed of small flat facets that can approximate a rounded shape, as shown in  FIG. 2B . The top portion  230  of the gemstone in  FIG. 2B  includes a series of flat facets that approximate a hemisphere shape. In one embodiment, the top portion  230  may comprise flat facets, except for one rounded facet in the center (table) of the gemstone. The bottom portion  280  of the gemstone in  FIG. 2B  includes a series of flat facets that approximates a cone, e.g., can be similar to a conventional round brilliant pavilion with a sharp point. 
     The disclosed spheroidal gemstone is empowered by the much-increased intensity of light reflecting from the focal point  204  of its gemstone as it sweeps across the lower half (relative to the orientation shown in  FIGS. 2A-2B ) of the gemstone on rotation of the gemstone. In some embodiments, such “self-illumination” focal point brilliant spheroidal gemstone can reach 180 diopters in lens power for a diamond. 
     In some embodiments, reflective basins  250 ,  260  can be included in the gemstone  200 . The reflective basins  250 ,  260  can be along the side of the pavillion (as shown), or may be closer to the bottom  208  of the gemstone  200 , in various implementations. The amount of reflected light back to the observer depends on the refractive index of the gemstone material and cut of the gem forming a focal point to self-illuminate the reflective facets and/or the reflective basins  250 ,  260  at the gemstone&#39;s base. According to various embodiments, the reflective basin can be convex (e.g., reflective basin  250 ), concave (e.g., reflective basin  260 ), or have any other shape, e.g., flat. In some embodiments, the reflective basins  250 ,  260  may be etches made into flat facets. For example, the flat facets can have any shape, including square, triangle, rectangle, hexagon, diamond, or any other shape. Curved facets can also have any shape, including concave or convex shapes, as shown in  FIGS. 2A-2B . 
     Light interaction with the spheroidal faceted gemstones of  FIGS. 2A-2B  is different than light interaction with a conventional round brilliant gemstone, such as shown in  FIG. 1 . With the disclosed spheroidal faceted gemstones, sunlight refracts into colored rays and unrefracted light upon entering the gemstone. In various embodiments, the spheroidal crown acts like a convex lens to form a focal point at or near the base of the gemstone. Intense colored rays and/or unrefracted sunlight refract on exiting the gemstone. In some embodiments, flat facets on the crown (and pavilion) of the spheroidal faceted gemstones act as a small prism to create a visible light spectrum with consistent sequences of red, orange, yellow, green, blue, and violet colors. In some implementations, this visible light spectrum may be observed on each flat facet when the gemstone is turned slowly. This spectrum of visible light colors may also be observed on a darker background around the intensely illuminated spheroidal faceted gemstones (with focal point created at or near the base). In some implementations, the gemstone crown may have a few hundred facets on the hemispheric surface, where each flat facet may be at a slightly different angle to the refracted sunlight and, thus, displays a different spectral color. The observer of the gemstone then sees random colors from the spectrum of colors that each flat facet displays. 
     Described herein is a new method of gem creation (or gem cutting) to improve the beauty of gemstones and gem materials by increasing the saturation of colors, the duration over which colors are observed in a gemstone as it is rotated, greater brightness, more numerous colors observed at one time, and many colors of the visible spectrum occurring with one position of the gemstone, in some embodiments. For example, each facet&#39;s reflection may contain all colors of the natural visible spectrum. New spectral color patterns and gem designs may occur due to enhanced spheroidal optics employed, as described in greater detail herein. 
     The spheroidal shape of the top of the gem and adjoining connected curvilinear surfaces act as a convex lens to focus the rays and brightness at or near the base of the gem. Basins included at the bottom of the gem are illuminated by this focused light. Light that reflect from said basins forms saturated color patterns and ultra-brightness for illuminating the gemstone. In some embodiments, light rays that enter the gemstone are reflected only a single time in the gemstone before exiting the gemstone (as opposed to the typical two or more reflections that occur in a round brilliant cut diamond), and thus have a shorter path to travel than flat faceting. Also, conventional gem cuts with multiple reflections within the gemstone may cause loss of light intensity. By providing a single reflection point or surface and shorter path for the light rays to travel, embodiments of the disclosure create ultra-brightness and brilliant colors radiating from the spheroidal gemstone. In some cases, longer lasting, rich colors are observed on rotation of the spheroidal gem, unrestricted by the need for connecting prisms, which cause chopped-off natural visible spectra, as in flat faceting of conventional gems. According to embodiments of the disclosure, the new, saturated colors and 3-D (three-dimensional) brilliance of gemstones simulate a celestial experience and are a wonder to behold. 
     The spheroidal shape of the top/crown of the gemstone  200  acts as a convex lens to focus the refracted colored rays and sunlight to a focal point at or near the base, which in turn reflects, only a single time, to cause intense colors and light to the observer. With this and other added enhancements described below, gems with unusually rich color patterns and unique designs may be created. In some embodiments, the spheroidal-shaped gemstone can include flat faceting to approximate spheroidal (i.e., curved) faceting. 
     Embodiments of the disclosure provide saturated colors with greater lasting duration in a gem as it is rotated, in addition to more sparkle in the gem to attract the eye. The disclosed embodiments allow for all the colors of the natural visible spectrum to be present at the same time. In some embodiments, the base of the gemstone may be painted with color, e.g., pastel or vivid “electric-light” colors, that sweep across the gem&#39;s basin, which may remain radiant on rotation of the gem. 
     In one embodiment, top portion  206 ,  230  of a spheroidal gemstone in  FIGS. 2A, 2B  can be formed similar to a surface ball lens. For a ball lens, the focal length can be described as a function of the refractive index of the ball lens and its diameter. The gemstone can be designed with overall spheroidal features that give an intense focal point in the gemstone  200 . In such a case, the focal point distance can be used to illuminate the base and/or reflective facets or reflective basins at this distance in the lower half of the gemstone, opposite to the incoming sunlight incident on the upper half (i.e., top  206 ) of the gemstone  200 , as shown in  FIG. 2A . This combination of new optical features (i.e., spheroidal gem design and formation of an intense focal point in the gemstone), transforms the gem material into a unique, shockingly beautiful gemstone. 
     Spheroidal gemstones, according to some embodiments of the disclosure, utilize a focal point for intense optical self-illumination giving more saturated tones of color, sparkle, and brightness from the base and/or reflective facets or small reflective basins. In some implementations, this creates a new internal source of light illumination in the gemstone (i.e., the focal point) and a new light intensity design dimension (LIDD) to consider for creation of beautifully different colored gem designs. LIDD is an intricate physical design of a gemstone and the facet arrangement and location on the gemstone that will govern the intensity of the refracted and reflected colors, brightness of the gemstone, and scintillation on rotation seen by the observer. LIDD also pertains to very small segments within the gemstone with special color or optical properties, highlighting in part, physical design or certain artistic features, and also mother-daughter pairs and adjacent gemstones. 
     In an embodiment, the distance from the center of a spheroidal gemstone to its focal point, that is, the focal length  270  of the gem, indicates where the reflective facets of a spheroidal gem should be located at the lower half of the gem, opposite to the incoming light. The location of facets at the focal point  204  results in self-illumination of the gemstone&#39;s facets, improved resolution of saturated colors, greater brilliancy of the gemstone packed into a small point or area. In some embodiments, two or more spheroidal gemstones can be arranged together (as described in greater detail herein), where a first gemstone imparts increased light illumination into a second gemstone, and the second gemstone reciprocates with additional color, body color, and sparkle (if a pair). Spheroidal gemstones may exhibit unusual spectral color patterns including: sparking rainbows, multicolored spectral basins, northern lights, rising and setting colored suns, pastel-colored gems, internal pin-point spectral rays, and colored bands. In some implementations, the disclosed design for a spheroidal gemstone that self-illuminates by forming a focal point within or near the base of the gemstone are also applicable to reflective signs, billboards, road markers, etc. 
     In some embodiments, small flat facets can be used to approximate a spheroidal shape. These small flat facets can be effectively spaced as small reflective basins.  FIGS. 3A-C  illustrate views of a focal point brilliant spheroidal gemstone for self-illumination according to an embodiment of the disclosure.  FIG. 3A  illustrates a top view of the spheroidal gemstone  300  showing a small table center surrounded by twelve (12) beveled facets in a first row. Surrounding the 12 beveled facets are three rows of triangles, each row of triangles increasing in size as a function of the distance from the small table center.  FIG. 3B  illustrates a side view of the spheroidal gemstone  300  of  FIG. 3A . The side view shows that the spheroidal gemstone  300  has a hemispehrical shaped crown  302  and a cone shaped pavilion  304 . The side view shows that the three rows of triangles increase in size until the girdle  306  of the spheroidal gemstone  300 . The cone shaped pavilion  304  includes elongated diamond-shaped facets that decrease in size from the girdle  306  of the spheroidal gemstone  300  to its culet  308 . At the base of the spheroidal gemstone, sixteen (16) elongated facets terminate at its culet  308 .  FIG. 3C  illustrates a bottom view of the spheroidal gemstone  300 . The 16 facets at the culet  308  are shown to be small, elongated and diamond-like in shape. 
     The gemstone design and dimensions in  FIGS. 3A-C  is provided as an example approximation to a spheroidal shaped gem. The small table center can be surrounded by more than 12 or less than 12 beveled facets, according to various embodiments. In addition, more than three rows of triangles may surround the beveled facets, according to various embodiments. Additionally, the elongated facets at the culet may be more than or less than 16, according to various embodiments. 
       FIGS. 4A-C  illustrate views of a focal point brilliant spheroidal gemstone  400  according to an embodiment of the disclosure.  FIG. 4A  illustrates a top view of the spheroidal gemstone  400  showing a small table center surrounded by twelve (12) triangular facets in a first row. Surrounding the 12 triangular facets are two rows of triangles, each row of triangles increasing in size as a function of the distance from the small table center.  FIG. 4B  illustrates a side view of the spheroidal gemstone  400  of  FIG. 4A , showing a hemispheroidally shaped crown  402  with a slightly cone shaped bottom  404 . The slightly cone shaped bottom  404  includes diamond-shaped facets that decrease in size from the girdle of the spheroidal gemstone. At the base of the spheroidal gemstone  400 , eight (8) elongated facets terminate at its culet  408 .  FIG. 4C  illustrates a bottom view of the spheroidal gemstone  400 . The 8 facets at the culet  408  are shown to be small, elongated and diamond-like in shape. The numbers of facets at each row of facets discussed above with respect to  FIGS. 4A-C  are provided as examples. 
     As previously discussed, a lens has a focal length. The inverse of the focal length is called the lens strength or lens power and is measured in diopters. That is, lens power in diopters (P) is provided by P=1/focal length (f) in meters. As an example, a 13.0 mm diameter diamond with a focal length of 5.544 mm (measured from the center of a spheroidal gem) is P=1/0.005544 meters. The lens power of this spheroidal gem is 180 diopters in strength but will vary with the refractive index of the gem material. An ordinary gemstone receives unfocused sunlight to illuminate the gemstone; by contrast, focusing of the light at a focal point such that it reflect back out the top of the gemstone (i.e., so-called “self-illumination”) occurs with spheroidal gemstones that are cut according to the present disclosure. Embodiments of the disclosure result in numerous intensely saturated spectral colors and, on rotation of the gemstone, shocking scintillation and enhanced brightness throughout the gemstone. In some embodiments, regions of color in the gemstone may be smaller in size, but have greater saturation of color, more numerous in occurrence, and much more intense in illumination compared to conventional gemstones. An example of a spheroidal gemstone, according to an embodiment of the disclosure, showing enhanced brightness and saturation of color is provided in  FIG. 5 . 
     In some embodiments, gemstone material is faceted into other spheroidal shapes besides ball lens shapes. These spheroidal shapes may include pear, oval, marquise, heart, hexagonal, trilliant, briolette shapes, each having a focal point and self-illumination of basal facets. 
     In some embodiments, darker gem materials (for example, smoky quartz) may be faceted to become self-illuminated (i.e., by a focal point) so as to be more adaptive as gemstones. Also, in some embodiments, cabochons may sparkle with color and brighten intensely with the disclosed focal point brilliant design (i.e., with a more spheroidal crown and a deeper pavilion). 
     Embodiments of the disclosure can be used to facet spheroidal gemstones to provide: (1) an increasing number of colors occurring in the gemstone; (2) longer lasting colors on gem rotation; (3) all colors of the natural visible spectrum displayed at one time; (4) saturated tones of color compared to flat faceted gemstones; (5) finer colors occur but much more intense; and (6) colors caused by refraction on entering the gemstone&#39;s spheroidal upper surface, and reflection of refracted colors and light from the gemstone&#39;s lower surface to all or a subset of facets on the gemstone. 
     Embodiments of the disclosure provide spheroidal faceting that creates centers of enhanced refraction in the top half of a gemstone (i.e., above the girdle) and areas of reflection at the bottom half of the gemstone. The enhanced refraction to a focal point within or at the base of the gemstone provides for additional color formation in the gemstone, and together with enhanced reflective basins in the lower half of the gemstone, these colors are reflected back to an observer providing a further increase in number of colors, saturation, and brightness that the observer receives from the gemstone. The spheroidal faceting according to embodiments of the disclosure provides self-illumination of enhanced reflective basins by beams of colored rays and, when combined with un-refracted sunlight, causes even stronger colors and brightness throughout the spheroidal gemstone that, in turn, radiates to the observer on rotation of the gemstone. Also, if the base of the gemstone is darkened on its underlying surface, a transparent gemstone will show a better color contrast and even faint colors (e.g., yellows and pinks) can be better seen in strong sunlight. 
     In an embodiment, a major axis of light illumination of a spheroidal gemstone can be made longer or shorter to accommodate the focal length of the gemstone to be inside the gemstone so that the focal point can self-illuminate reflective facets or reflective basins at the base of the gem on rotation with intense focal point light. Bright, rich colors with intense gem brightness and dazzling scintillation on rotation provide for more radiant gemstones. Embodiments of the disclosure include spheroidal optic features for multiple styles of gem cuts designed into the external surface of the gemstone, which enhance refraction and reflection. This gives more numerous, brighter, saturated, and longer-lasting spectral colors in the gemstone with different designs than in conventional art. 
     In some embodiments, colors reflect from various shaped and sized facets on the lower half of a spheroidal gemstones. In some embodiments, numerous reflective facets show brilliant, saturated colors of both individual and rainbow designs of the visible spectrum in any position of the gemstone. In some embodiments, all colors in the visible spectrum may occur, ranging from violet to red. 
     In some embodiments, a gem with dual pair of refractive features on the top surface of the gem and approximately diagonally opposite reflective basin designs, sculptured around the bottom half of the gemstone, may exhibit spectacular continuous color on rotation. The spectral colors caused by refractive features faceted into the top half of the gemstone&#39;s surface, and the reflective basins and surfaces and optic-ornamental designs faceted into diagonally opposite positions into the lower half of the gemstone give increased spectral patterns of bright, saturated colors and new unique designs, which may be seen through the top half of the gemstone. 
     Optic-ornamental designs of gemstones according to embodiments of the disclosure may include, but are not limited to: a flower, a bird, an animal, a fish, a flag, a map, a picture, a letter, a number, a symbol, a word, a phrase, an emblem, one or more initials, a name, a country, a location, and/or a logo, etc. For surface features enhancing refraction, the gemstone may be faceted with an overall spheroid or rounded cone shape with additional convex lens-like features, which may include: hemispheres, mushroom shapes, domes, ridges, spheroidal pentagonal polished facets and concave-like dimples, and small caldera structures. 
     In some embodiments, the addition of horizontal and/or vertical rounded bands or grooves around the top half of the gemstone, the mid-section, and/or near the base of the gemstone also enhance refraction in the gemstone. 
     Prominent colors in gemstones sculptured or faceted according to embodiments of the disclosure are created by, but not limited to: (1) refraction and a convex focused lens effect of the overall enhanced spheroidal gem and many other spheroidal surface features, (2) reflection from flat facets, (3) pin-point internal focused colored rays similar to water waves focusing before a parabolic barrier, (4) prism effect due to varying thickness of gem material in the gemstone, and (5) light interference effects of spectra. 
     Some examples of surface features enhancing reflection to occur include, but are not limited to: headlight, tail light, flash light concave reflectors, including a parabolic pavilion, and curved or spheroidal facets, basins, bowls, cups, valleys, oval reflective curved surfaces (small cirques) around the bottom half, and perhaps a central dome(s) or optical ornamental display, to reflect colored light upward from the base throughout the gem. An observer, due to the overall spheroid or rounded hemisphere shape on the surface, acting as a lens at the top of the gem, may easily see these features with a 10× hand lens. Prisms of thinning gem material around gem edges can also cause bright refractive colors to appear in the gem. Additionally, in some cases, darkening the base of the gem or its underlying surface makes light colors, faint pinks and yellows, easier to be seen especially under strong sunlight. 
     With water waves approaching a two-dimensional parabolic barrier, the wave energy is reflected off the barrier to a point in front of the barrier before the wave energy dissipates around the focal point. As sunlight mainly exhibits wave motion, in a three-dimensional gemstone spheroid, light waves may exhibit an internal point of focus inside the walls of the gem similar to the parabolic barrier approached by water waves. This focal point may cause a beam of bright colored rays to originate from a single point inside the gem. As the gem is slowly rotated, a different color occurs adjacent to the color just observed and is the next color along a spectrum of visible light. The new bright color originates from the same area, but with a different wavelength due to a slightly different path through the gem. This is the next colored ray of a spectrum occurring at an internal focal point in the gem. Embodiments of the invention exhibit sparkling examples of colors suddenly appearing from a point within the gemstone and changing colors on rotation of the gem, give rising and setting suns of varying spectral colors. 
     Prominent colors in gemstones may be created by, but not limited to: refraction and a convex focused lens effect of the overall enhanced spheroidal gem and many other spheroidal surface features on it, reflected colors from enhanced basins, pin-point internal focused colored rays similar to water waves focusing before a parabolic barrier, prism effect due to varying thickness of gem material in the gemstone, and light interference effects of spectra. Other features which may create color include but are not limited to: an undulating basin surface or pin point array at the base of the basin, a ringed or dimpled basin, reflective gem walls, internal partition of borders or gem faces, one or more central domes or optical ornamental features, very small caldera-like structures, rounded horizontal and vertical bands, grooves and small parallel growth striations which imitate a colorful diffusion grid. 
     With the embodiments of the disclosure, sunlight is refracted on entering the gemstone&#39;s surface, strongly focused by the spheroidal crown to the focal point near its base (i.e., so-called “focal point brilliant” cut), and reflected only once inside the gem (as compared to twice for flat faceted gems, such as the round brilliant), and refracted once again on leaving the gemstone. Inexpensive non-gem materials such as glass, marbles, plastic, acrylic, plexiglass, etc., can also be faceted in spheroidal fashion as described above. In various embodiments, any non-opaque natural or man-made gem material or solid non-gem material may be used. 
     Possible shapes for spheroidal gemstones in addition to hemispheric/cone include transparent peeled mandarin orange or a transparent jelly donut. These two possible shapes can exhibit a bulbous top and/or bottom surface. The feature of sphericity in the gemstones of these shapes may allow formation of a focal point and self-illumination that causes enhanced reflection to occur, resulting in increased rich colors and brightness originating in the gem. 
     In some embodiments, spheroidal gemstones may be about as deep as they are wide. In some embodiments, small lens-like spheroids may be sculptured or faceted on the larger gem spheroid for enhanced refractive features and magnification at the top of the gem to see small gem features at the base and enhanced curved reflective basins around the base of the gemstone for brilliance and color radiance throughout the gemstone. In some embodiments, gem surfaces may exhibit a mirror-like finish which enhances refraction and reflection and adds quality of gem workmanship. 
     Spheroidal gemstones according to embodiments of the disclosure may reduce wastage, which can occur up to 60% during the gem cutting process. Thus, while faceting to obtain spheroidal shapes according to some embodiments of the disclosure, less gem material may be wasted than the present “V” shape of the round brilliant cut stones. In some embodiments, the weight of the spheroidal gemstones is heavier than their flat cut counterparts. 
     Example embodiments of spheroidal gemstones are provided in the accompanying figures.  FIG. 6A  illustrates a top view of a smooth dome  602  hemispheric gem with slightly concave sides  604  according to an embodiment of the disclosure.  FIG. 6B  illustrates a side view of the smooth dome  602  hemispheric gem showing narrow slits  606  between slightly concave sides  604  of the hemispheric gem.  FIG. 6C  illustrates a bottom view of the smooth dome hemispheric gem showing convex cups  608  of transparent gem material between sectors at the base of the gem. 
       FIG. 7A  illustrates a top view of a gem with a spheroid top  702  according to an embodiment of the disclosure.  FIG. 7A  shows that the gem includes bulbous facets  704  at the base and beveled bands  706  sloping down.  FIG. 7B  illustrates an oblique view of the gem with the spheroid top  702  of  FIG. 7A .  FIG. 7B  shows that the beveled bands  706  sloping down are at the midsection of the gem, decreasing gem thickness, and the bulbous reflective basins  704  are at the base of the gem.  FIG. 7C  illustrates a bottom view of the gem of  FIG. 7A , showing slightly convex base with bulbous reflective basins  704  exterior. 
       FIG. 8A  illustrates a top view of a linearly arranged row of gem spheroids according to an embodiment of the disclosure. The row of gem spheroids include some gems with concentric striations  802  on mirror smooth surface.  FIG. 8B  illustrates a side view of the linearly arranged row of gem spheroids of  FIG. 8A . The row of gem spheroids may exhibit uneven thickness and internal dimensions of the spheroids, which can cause unusual refractive colors. 
       FIG. 9A  illustrate a top view of circularly arranged gem spheroids according to an embodiment of the disclosure. The circularly arranged gem spheroids can include a double row of gem material offset to cause reflection in opposite spheres after refraction.  FIG. 9B  illustrates a side view of the circularly arranged gem spheroids of  FIG. 9A . 
       FIG. 10A  illustrates a top view of a gem according to an embodiment of the disclosure. The gem includes a smooth hemispheres  1002  and two striations  1004  above its base.  FIG. 10B  illustrates a lateral/side view of the gem in  FIG. 10A . The smooth hemispheres  1002  of the gem form bulbous curved sectors with the two striations  1004  near the bottom of the smooth hemispheres  1002 . The base of the gem is shown to be convex.  FIG. 10C  illustrates a bottom view of the gem in  FIG. 10A , showing an overall convex base with many smaller hemispheres  1006  varying in depth over the convex base. 
       FIG. 11A  illustrates a top view of a gem according to an embodiment of the disclosure. The gem is shown to exhibit a faint bulges  1102  (e.g., pentagonal or other shape bulges), a mirror finish  1104 , and multiple striations  1106 .  FIG. 11B  illustrates a side view of the gem of  FIG. 11A . The side view illustrates the multiple striations  1106  further showing banded striations  1108  below the multiple striations  1106 . The surface of the gem is shown to include faint indentations  1110 .  FIG. 11C  illustrates a bottom view of the gem of  FIG. 11A  showing convex bulges  1112  on the base of the gem.  FIG. 11D  illustrates an end view of the gem of  FIG. 11A  showing the banded striations  1108  in relation to the multiple striations  1106 . 
       FIG. 12A  illustrates a top view of an oval spheroidal gem according to an embodiment of the disclosure. The oval gem exhibits a smooth hemisphere  1202  with few curvalinear striations  1204 .  FIG. 12B  illustrates a side view of the gem of  FIG. 12A , showing decreasing bands  1206  of transparent gem material. The side view also shows a deep thickness of the oval gem where the depth of the gem is approximately equal to the width of the gem.  FIG. 12C  illustrates a bottom view of the gem of  FIG. 12A , showing concentric indented bands  1208 . Curved bands  1210  above mid-section of the oval gem and varying thickness in the gem may cause of a northern lights pattern to be viewed by an observer on the opposite side of the thick oval gem shown in  FIGS. 12A-12C . 
       FIG. 13A  illustrates a top view of a double gem according to an embodiment of the disclosure. The double gem includes beveled bands around each center.  FIG. 13B  illustrates a side view of the double gem of  FIG. 13A  showing the beveled bands  1302  around each center  1304  and a band with a polygonal  1306  design.  FIG. 13C  illustrates a bottom view of the gem of  FIG. 13A  showing convex basin sectors  1308  and bands of polygonal  1306  gem material. 
       FIG. 14A  illustrates a top view of a gem according to an embodiment of the disclosure. The gem is shown to include central convex lens  1402  with twelve rounded sectors  1404  each including about a 30-degree angle at an opposite end. The gem can be faceted to be symmetrical in some implementations.  FIG. 14B  illustrates a side view of the gem of  FIG. 14A .  FIG. 14C  illustrates a first embodiment of a bottom view of the gem of  FIG. 14A , showing “V” shaped cuts  1406  into the gem&#39;s base with a central convex basin  1408  and concave grooves  1410  in the bottom of the gem.  FIG. 14D  illustrates a second embodiment of a bottom view of the gem of  FIG. 14A , showing “V” shaped cuts  1412  into the gem&#39;s base with a central concave  1414  basin and concave grooves  1416  at the bottom of the gem. 
       FIG. 15A  illustrates a top view of a spheroidal gem with beveled bands according to an embodiment of the disclosure. In one embodiment, the gem has a spheroidal top with two or three beveled bands  1506  above its midsection.  FIG. 15B  illustrates a side view of the gem of  FIG. 15A . The gem includes a convex base  1502  and top  1504 , with two or three beveled bands  1506  on top and small hemispheres  1508  on the base.  FIG. 15C  illustrates a bottom view of the gem of  FIG. 15A . The base of the gem is convex with some striations below the midsection and small hemispheres  1508  lining the base. 
       FIG. 16A  illustrates a top view of an oval spheroidal gem with beveled cuts according to an embodiment of the disclosure. The gem includes oval shaped transparent layers with the first three layers  1602 ,  1604 ,  1606  being mirror smooth and the next four layers  1608  having narrow, beveled cuts. The gem has a clear top and some indentations. Furthermore, the gem includes approximately four or five layers of narrow downward sloping beveled surfaces at, e.g., 20°, 30°, 50°, 75°, 90°.  FIG. 16B  illustrates a side view of the gem of  FIG. 16A . The side view shows an overall flattened oval spheroid with four rows of beveled surfaces  1608  on a top half and spheroidally beveled surfaces  1610  on a lower half. In an embodiment, sunlight refracts on entering the gem and reflected colors have a radial pattern around the center of the gem.  FIG. 16C  illustrates a bottom view of the gem of  FIG. 16A , showing a convex lower half with beveled surfaces at, e.g., 0°, 20°, 40°, 60°, 80°, 90°. The bottom view of the gem may resemble an oval gem cut. 
       FIG. 17A  illustrates a top view of a gem according to an embodiment of the disclosure.  FIG. 17B  illustrates a side view of the gem of  FIG. 17A .  FIG. 17C  illustrates a bottom view of the gem of  FIG. 17A . The gem includes a faceted top portion  1702  (e.g., shaped like a sphere) and an faceted bottom portion  1704  (e.g., shaped like a flattened oval). 
       FIG. 18A  illustrates a top view of a gem according to an embodiment of the disclosure. The gem exhibits a flat slab  1802 , has a cocoon-like structure, and faint intersection lines  1804 . In an example, seven faint vertical intersection lines  1804  may be sculptured or faceted into the gem.  FIG. 18B  illustrates a side view of the gem of  FIG. 18A . The gem may have a mirror finish with a few striations  1806 . Faint bands  1808  may be etched in the lower half of the gem.  FIG. 18C  illustrates a bottom view of the gem of  FIG. 18A , showing a few striations and vertical bands.  FIG. 18D  is an end view of the gem in  FIG. 18A . 
       FIG. 19A  illustrates a top view of a gem according to an embodiment of the disclosure. The gem is shown to exhibit a raised center  1902 .  FIG. 19B  illustrates a side view of the gem of  FIG. 19A , showing spheroidal bands  1904  around the gem.  FIG. 19C  illustrates a bottom view of the gem of  FIG. 19A  showing slightly convex basin with hemispheres  1906  acting as reflective cups or bowls. 
       FIG. 20A  illustrates a top view of a gem with a bulbous top  2002  according to an embodiment of the disclosure.  FIG. 20B  illustrates a side view of the of  FIG. 20A  showing bulbous sides  2004 .  FIG. 20C  illustrates a bottom view of  FIG. 20A , showing a convex base  2006  at a central area of the gem. 
     Some examples of refractive surfaces according to embodiments of the disclosure include, but are not limited to:
         a. A few small lens, or many, centrally located, radially partitioned or not, on top half of hemisphere,   b. Faint convex surfaces on top half of gem,   c. Small dimples on convex surface,   d. Medium sized, segmented lens centrally located on top half of gem,   e. Thin overlapping solid layers on top of gem surfaces cause sunlight to refract,   f. Small, rounded caldera (volcanic vent-like structures) with concave features,   g. Complete top hemisphere of gem-polished,   h. Spheroidal polygonal facets on top portion of a gem, a few horizontal rows, or area wide,   i. A few horizontal bands or random horizontal and some vertical rounded bands, grooves, or striations with a few around the top half of the gem, more at mid-section, and most below midsection, cause refraction to occur,   j. Bulbous pillows of gemstone material on the top and bulbous lenses of gem material symmetrically placed near midsection and below enhance refractive colors to occur. On top half, lenses, domes, mushroom shapes, circular ridges and valleys, dimples, and circular rimed lower areas or, sections thereof, (rounded); contribute to refraction in the lower half of the gem,   k. Thickening or thinning of gem material, mainly at gem edges, can cause colors to appear, as with a prism, or   l. Thickening rounded top rims may give 1st, 2nd, 3rd order colors at gem&#39;s reflective base.       

     Some examples of reflective surfaces, for light and color, according to embodiments of the disclosure include, but are not limited to:
         a. A round crown, cone-like shape of pavilion, forms reflective focal point facets,   b. Any curvilinear surface reflecting colored rays or brightness,   c. Cone-like or less than spheroidal shape of pavilion of the gemstone,   d. Enhanced cups, bowls, basins (various sizes) and shapes (round, oval, elongated),   e. Cirques (small oval convex basins),   f. Caldera (round cones) in the surface-wider than deep, with round edges,   g. In lower half of gem, spheroidal facets or hemispheres with varying sizes, convex out for reflective basins,   h. Internal intersections of faces, corners, curves, junctions in gem,   i. Polygonal spheroidal surfaces in the lower half of gem, convex out for reflective basins,   j. Central lens at base either convex out or concave in, or   k. Flat faceted pavilion facets suffice, but a spheroidal convex basin, or hemispheres with varying sizes, convex out, may give more saturated reflected colors       

     Spheroidal gemstones may display the following characteristics: 1. An increasing number of colors occurring in the gemstone. 2. Longer lasting colors on gem rotation. 3. All colors of the natural visible spectrum displayed at one time, 4. A greater saturation of color, particularly with violets, blues, and greens, and 5. Brighter gems with increased scintillation on rotation. 
     With some embodiments of the disclosure, all colors of the natural visible spectrum may be observed with the gemstone in a fixed position, due to full spectrum refraction and reflection in the gemstone. Areas of color may be smaller in size, but more saturated in color and more numerous in occurrence in a spheroidal enhanced gemstone, than in a flat faceted gem. As the overall gem is spheroidal or augmented by lens-like structures, or may be slightly cone shaped, small features near the base in the gem are magnified and are visible with the naked eye or with a 10× hand lens. The travel path of light rays may be shorter from being reflected only once in the spheroidal gemstone, thus there is less chance of loss of light in the gemstone than presently occurs with flat faceted gemstones, adding to brighter gems, greater colors saturation and greater brilliance throughout the gemstone. All colors of the natural visible spectrum may be displayed continuously and simultaneously with shocking scintillation as the gemstone is rotated 360°. 
     Unusual spectral color patterns and gem designs may occur due to spheroidal optic faceting of gems according to embodiments of the disclosure, resulting in, but not restricted to: vivid ‘electric-light’ colors, sparkling rainbows, multicolored spectral basins, northern lights, rising and setting colored suns, pastel-colored gems, internal pin-point spectral rays, colored bands, brighter gemstone, enhanced scintillation and optic-ornamental features as the focal point sweeps across the gem&#39;s reflective facets or basins on rotation of the gem. Unique physical gem shapes occur beyond those presently cut with the above-mentioned more saturated colors and brightness radiating throughout the gemstone to the observer with a 3-dimensional effect occurring in the gemstone. 
     Exemplary materials for sculpturing according to the present disclosure are inexpensive, transparent or semitransparent, and light to medium colored gemstones. Other darker stones, natural or manmade, gem or non-gem materials may be illuminated by intense focal point light in the gemstone with sparkling saturated colors and brightness to give more adaptive darker potential gemstones in the future. 
     Spheroid and spheroidal as used in the present disclosure refer to shapes that resemble but are not necessarily spheres, including but not limited to: perfect spheres, ellipsoids, spheres with additional features external or internal to the sphere surface, ellipsoids with additional features external or internal to the ellipsoid surface, and a series of flat facets that approximate a smooth spheroidal surface. 
       FIGS. 21A-33A  illustrate examples of gemstones created according to the present disclosure, according to various embodiments. The gemstones shown in  FIGS. 21A-33A  are merely examples, and not meant to limit the scope of the disclosure. Also, some of the examples shown in  FIGS. 21A-33A  include air bubbles, as some of the stones are cut from sample glass marbles that included air bubbles. The air bubbles are not necessary to the disclosure, and in some embodiments better (more brilliant) results occur if there are no air bubbles. 
     In general, in the gemstones in  FIGS. 21A-33A , the overall spheroidal crown (i.e., top portion of the gemstone) initiates formation of a focal point in the pavilion (i.e., bottom portion of the gemstone). The pavilion, which includes the axis of light, forms a focal point to illuminate reflective facets. Although the overall gem shape, especially the crown, is spheroidal, the facets may be flat due to the fact that it is difficult to form convex or concave facets on spheroidal surfaces, although convex or concave facets are part of the present disclosure. Flat facets are merely one embodiment. The shape of the facets can be polygons of any shape having three (3) sides and greater (e.g., square, rectangular, triangular, pentagonal, diamond, etc.) The location of reflective facets at the focal point gives best self, supra-illumination of spheroidal gemstones and best resolution of saturated colors, brilliancy, and scintillation on gem rotation. 
       FIG. 21A  illustrates a top view of a round gem,  FIG. 21B  illustrates a side view of the round gem in  FIG. 21A , and  FIG. 21C  illustrates a bottom view of the round gem in  FIG. 21A . 
       FIG. 22A  illustrates a top view of a round gem,  FIG. 22B  illustrates a side view of the round gem in  FIG. 22A , and  FIG. 22C  illustrates a bottom view of the round gem in  FIG. 22A . 
       FIG. 23A  illustrates a top view of an oval gem,  FIG. 23B  illustrates a side view of the oval gem in  FIG. 23A , and  FIG. 23C  illustrates a bottom view of the oval gem in  FIG. 23A . 
       FIG. 24A  illustrates a top view of a round gem,  FIG. 24B  illustrates a side view of the round gem in  FIG. 24A , and  FIG. 24C  illustrates a bottom view of the round gem in  FIG. 24A . 
       FIG. 25A  illustrates a top view of a round yellow gem,  FIG. 25B  illustrates a side view of the round yellow gem in  FIG. 25A , and  FIG. 25C  illustrates a bottom view of the round yellow gem in  FIG. 25A . 
       FIG. 26A  illustrates a top view of a pear-shaped gem,  FIG. 26B  illustrates a side view of the pear-shaped gem in  FIG. 26A , and  FIG. 26C  illustrates a bottom view of the pear-shaped gem in  FIG. 26A . 
       FIG. 27A  illustrates a top view of a heart-shaped gem,  FIG. 27B  illustrates a side view of the heart-shaped gem in  FIG. 27A , and  FIG. 27C  illustrates a bottom view of the heart-shaped gem in  FIG. 27A . 
       FIG. 28A  illustrates a top view of a princess cut gem,  FIG. 28B  illustrates a side view of the princess cut gem in  FIG. 28A , and  FIG. 28C  illustrates a bottom view of the princess cut gem in  FIG. 28A . 
       FIG. 29A  illustrates a top view of a hexagonal gem,  FIG. 29B  illustrates a side view of the hexagonal cut gem in  FIG. 29A , and  FIG. 29C  illustrates a bottom view of the hexagonal cut gem in  FIG. 29A . 
       FIG. 30A  illustrates a top view of a trilliant-shaped yellow gem,  FIG. 30B  illustrates a side view of a trilliant-shaped yellow gem in  FIG. 30A , and  FIG. 30C  illustrates a bottom view of the trilliant-shaped yellow gem in  FIG. 30A . 
       FIG. 31A  illustrates a top view of a briolette cut gem,  FIG. 31B  illustrates a side view of the briolette cut gem in  FIG. 31A , and  FIG. 31C  illustrates a bottom view of the briolette cut gem in  FIG. 31A . 
     Table 1 below summarizes features of the designs shown in  FIGS. 21A-31C . 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Gem 
                   
                 Facets 
                 No. of 
                   
               
               
                   
                 Description/ 
                   
                 just 
                 Facets 
                   
               
               
                   
                 Shape 
                 Table Facet 
                 Below 
                 Around 
                   
               
               
                 FIGS. 
                 (Material) 
                 Description 
                 Table 
                 Culet 
                 Notes on gemstone 
               
               
                   
               
             
            
               
                 FIGS. 
                 Round gem 
                 Small, round, 
                 12 
                 12 
                   
               
               
                 21A-21C 
                 (glass) 
                 flat table 
                 polygons 
                 diamond 
                   
               
               
                   
                   
                   
                   
                 shape 
                   
               
               
                 FIGS. 
                 Round gem 
                 Small, round, 
                 12 
                 8 
                   
               
               
                 22A-22C 
                 (glass) 
                 flat table 
                 triangles 
                 diamond 
                   
               
               
                   
                   
                   
                   
                 shape 
                   
               
               
                 FIGS. 
                 Oval gem 
                 Small oval flat 
                 12 
                 8 
                   
               
               
                 23A-23C 
                 (glass) 
                 table 
                 polygons 
                 diamond 
                   
               
               
                   
                   
                   
                   
                 shape 
                   
               
               
                 FIGS. 
                 Round gem 
                 Small, round  
                 12 
                 16 slim 
                 Bright colors 
               
               
                 24A-24C 
                 (cubic 
                 flat table 
                 polygons 
                 diamond 
                   
               
               
                   
                 zirconia) 
                   
                   
                 shape 
                   
               
               
                 FIGS. 
                 Round gem 
                 Small, round  
                 12 
                 16 slim 
                 Bright colors 
               
               
                 25A-25C 
                 (yellow cubic 
                 flat table 
                 polygons 
                 diamond 
                   
               
               
                   
                 zirconia) 
                   
                   
                 shape 
                   
               
               
                 FIGS. 
                 Pear shape 
                 No table,  
                 Square 
                 7 
                   
               
               
                 26A-26C 
                 (glass) 
                 Square facets  
                 facets 
                 diamond 
                   
               
               
                   
                   
                 on top 
                 top 
                 shape 
                   
               
               
                 FIGS. 
                 Heart shape 
                 No table.  
                 Square 
                 3 
                 Gem has triangular 
               
               
                 27A-27C 
                 (glass) 
                 Square facets  
                 facets 
                 polygons 
                 shape to pavilion;  
               
               
                   
                   
                 on top 
                 top 
                   
                 3 facets form base. 
               
               
                 FIGS. 
                 Princess cut 
                 No table.  
                 Polygon- 
                 8 slim 
                 Complex structure 
               
               
                 28A-28C 
                 (glass) 
                 Square facets. 
                 faceted 
                 triangles 
                 near culet 
               
               
                   
                   
                   
                 top 
                   
                   
               
               
                 FIGS. 
                 Hexagonal 
                 No table; flat, 
                 9 five- 
                 12 slim 
                 Very brilliant  
               
               
                 29A-29C 
                 cut (yellow 
                 very small facet 
                 sided 
                 diamond 
                 colors 
               
               
                   
                 cubic 
                 on top (9 sides) 
                 polygons 
                 facets 
                   
               
               
                   
                 zirconia) 
                   
                   
                   
                   
               
               
                 FIGS. 
                 Trilliant cut 
                 No table. Very 
                 6 four- 
                 6, four- 
                 Triangular  
               
               
                 30A-30C 
                 (yellow cubic 
                 small triangles 
                 sided 
                 sided 
                 gem gives good  
               
               
                   
                 zirconia) 
                 with (6 sides) 
                 facets 
                 facets 
                 color, sparkle, 
               
               
                   
                   
                   
                   
                   
                 and beauty 
               
               
                 FIGS. 
                 Briolette cut 
                 Small, flat, 12 
                 12 four- 
                 12 facets 
                 Transparent, 
               
               
                 31A-31C 
                 (glass) 
                 sided table. 
                 sided 
                 diamond 
                 elongated,  
               
               
                   
                   
                   
                 facets 
                   
                 glass gem 
               
               
                   
               
            
           
         
       
     
       FIG. 32  illustrates a cross-section of a focal point brilliant spheroidal faceted gemstone  3200  according to yet another embodiment of the disclosure. The gemstone  3200  includes a hemispheroidal crown  3202  (i.e., from the top of gemstone to girdle  3204 ) that creates a focal point  3210  at the base  3212  of the gemstone  3200 , as described herein. In the embodiment shown, the base  3212  of the gemstone  3200  comprises a sharp point. In other embodiments, the base  3212  may be a small flat surface or slightly rounded with small facets. The gemstone  3200  includes a pavilion  3208 . In one embodiments, the pavilion  3208  may be cone-shaped, as shown. In one implementation, the pavilion  3208  may be similar to that of a present-day round brilliant pavilion. 
     The gemstone  3200  also includes a faceted band  3206  below the girdle  3204  and above the pavilion  3208 . The faceted band  3206  is not found in present-day round brilliant cuts. The faceted band may comprise (from top to bottom) a first row of right-angle triangle facets, a second row of four-sided facets, and a third row of triangle facets, in the embodiment shown. Other embodiments having fewer or more rows for facets in the faceted band  3206  are within the scope of the disclosure. In some embodiments, any shape facets can be used in the faceted band  3206 . In some implementations, the faceted band  3206  provides additional sparkle and saturated colors to edges of the gemstone  3200 , while the base  3212  that corresponds to the focal point  3210  gives brilliant sparkle and saturated colors elsewhere throughout the gemstone  3200 . 
       FIG. 33A  illustrates a top view of a spheroidal faceted gemstone of  FIG. 32 ,  FIG. 33B  illustrates a side view of the spheroidal faceted gemstone in  FIG. 33A , and  FIG. 33C  illustrates a bottom view of the spheroidal faceted gemstone in  FIG. 33A . 
       FIG. 34  is a method for faceting a gemstone, according to one embodiment. 
     The method includes shaping a top portion of the gemstone as a hemisphere (or other spheroidal shape). The top portion acts as a refractive surface for light incident on the top portion and focal point lens originator (step  3402 ). The method further includes shaping a bottom portion of the gemstone as a cone, the cone acting as an axis of light and a reflective surface for focal point light incident on a surface in the cone (step  3404 ). 
     As such, incident light that interacts with the spheroidal top portion is focused to a focal point in the bottom portion. The light reflects once from the bottom portion and exits the gemstone out through the top portion of the gemstone. 
     As described herein, the dimensions of the gemstone may be calibrated based on the refractive index of the gem material. 
     In some embodiments, facets coinciding with the top portion (e.g., hemisphere) are cut into and aligned with the curved hemispheroidal top portion. Facets of the pavilion are cut on its cone-like curved surface and terminate at the culet. The focal point (i.e., point of maximum illumination crossing the axis of light in the pavilion) is where additional reflective facets can be located in the gemstone for additional resolution of reflective color and light upward through the surface facets of the top portion. The focal point crates a source of intense illumination to power the gemstone, which brightens the gemstone and gives brilliant, saturated colors in the gemstone. 
     Multiple-Gemstone Arrangements 
     In some embodiments, two or more gemstones that are faceted such as to create a focal point at or near the base of the gemstone (as described herein) can be arranged relative to one another in one jewelry piece. In some implementations, a largest gemstones of the arrangement may be referred to as the “mother” gemstone(s), where the other gemstones of the arrangement may be referred to as the “daughter” gemstone(s). 
       FIGS. 35A-35C  illustrate views of an arrangement of two spheroidal faceted gemstones according to an embodiment of the disclosure, where  FIG. 35A  is a top view,  FIG. 35B  is a side view, and  FIG. 35C  is a bottom view. As shown, a first gemstone  3502  (“mother”) is coaxially aligned along axis  3506  with a second gemstone  3504  (“daughter”), such that the light axis of the first first gemstone  3502  is the same as the light axis of the second first gemstone  3504 , i.e., light axis  3506 . The first gemstone  3502  is arranged above the second gemstone  3504  relative to the direction  3508  of incident light towards the gemstone arrangement. In one embodiment, the first gemstone  3502  and the second gemstone  3504  are made from the same gem material. In other embodiments, the first gemstone  3502  and the second gemstone  3504  are made from different gem materials. In various embodiments, the gemstones  3502 ,  3504  may have rounded surfaces or flat facets. In various embodiments, the bottom of the gemstones  3502 ,  3504  may be a sharp point, flat facet, or rounded bottom formed of a series of flat facets, or any other shape. 
     In one embodiment, when incident light enters the arrangement along direction  3508 , the light interacts with the spheroidal crown of the first gemstone  3502  to create a focal point. In some configurations, the arrangement of the two gemstones can be such that the focal point of light interacting with the first gemstone  3502  is at the top (table) of the second gemstone  3404 . In other embodiments, the focal point diameter corresponds to the culet of the first gemstone  3502 . In some implementations, the diameter of the culet of the first gemstone  3502  is about equal or smaller in diameter to a diameter of a table of the second gemstone  3504 . For example, the diameter of the culet of the first gemstone  3502  may be about 1-3 mm. In a single gemstone arrangement, a sharp point with narrow facets at the base of the gemstones may give good color and uniform brilliance across the crown. In a mother-daughter pair, a sharp point on the mother gemstone may interfere with acquiring colors and sparkle from the daughter; hence, a slightly rounded base with small flat facets for the mother gemstone may provide better color and sparkle acquisition from the daughter gemstone. 
     Some of the light that enters the first gemstone  3502  will be refracted such that it enters the second gemstone  3504 . Other light may enter the second gemstone  3504  directly without first entering the first gemstone  3502 . Light that enters the second gemstone  3504  is refracted to a focal point at the base of the second gemstone  3504 , and then reflected back out the top of the second gemstone  3504 . The light exiting the second gemstone  3504  then enters the first gemstone  3502 , and then exits the first gemstone  3502 . In some implementations, the colors radiating from the first (mother) gemstone  3502  in the two-gemstone arrangement are more numerous than from a single gemstone itself, more saturated in color, more intense in illumination, may be more evenly spaced across the crown of the first (mother) gemstone  3502 , and the body color of the second gemstone  3504  is acquired by the first gemstone  3502 , unless the second gemstone  3504  is colorless. In the disclosed arrangement, both gemstones  3502 ,  3504  may exhibit excellent beauty in colors and brilliance. 
       FIGS. 36A-36C  illustrate views of an arrangement of two spheroidal faceted gemstones according to an embodiment of the disclosure, where  FIG. 36A  is a top view,  FIG. 36B  is a side view, and  FIG. 36C  is a bottom view. As shown, a second gemstone  3604  (“daughter”) is aligned along a light axis  3606  that is perpendicular to a light axis  3610  of the first gemstone  3602  (“mother”). In one embodiment, the first gemstone  3602  and the second gemstone  3604  are made from the same gem material. In other embodiments, the first gemstone  3602  and the second gemstone  3604  are made from different gem materials. For example, when the second gemstone  3604  is colored and the first gemstone  3602  is colorless, the second gemstone  3604  can impart color to the first gemstone. When incident light enters the arrangement along direction  3608 , the light interacts with the second gemstone  3604  and reflects from a focal point within the second gemstone  3604 . The reflected light from the focal point within the second gemstone  3604  then illuminates the first gemstone  3602 . In various embodiments, the gemstones  3602 ,  3604  may have rounded surfaces or flat facets. In various embodiments, the bottom of the gemstones  3602 ,  3604  may be a sharp point, flat facet, or rounded bottom formed of a series of flat facets, or any other shape. Both gemstones  3602 ,  3604  may have sharp points to reflect light to their respective crowns. 
       FIGS. 37A-37C  illustrate views of an arrangement of two spheroidal faceted gemstones according to an embodiment of the disclosure, where  FIG. 37A  is a top view,  FIG. 37B  is a side view, and  FIG. 37C  is a bottom view. As shown, a second gemstone  3704  (“daughter”) is aligned along a light axis  3706  that is at a 45° angle relative to a light axis  3710  of the first gemstone  3702  (“mother”). The second gemstone  3704  is arranged below and to the side of the first gemstone  3702  and is angled up towards the first gemstone  3702  at a 45° angle. In one embodiment, the first gemstone  3702  and the second gemstone  3704  are made from the same gem material. In other embodiments, the first gemstone  3702  and the second gemstone  3704  are made from different gem materials. When incident light enters the arrangement along direction  3708 , some of the light interacts with the second gemstone  3704  and reflects from a focal point within the second gemstone  3704 . The reflected light from the focal point within the second gemstone  3704  then augments illumination in the first gemstone  3702 . In various embodiments, the gemstones  3702 ,  3704  may have rounded surfaces or flat facets. In various embodiments, the bottom of the gemstones  3702 ,  3704  may be a sharp point, flat facet, or rounded bottom formed of a series of flat facets, or any other shape. Once again, to reflect upward as much light as possible to both crowns, sharp, even facets may be used. 
     In some embodiments, both the first (“mother”) and the second (“daughter”) gemstones shown in  FIGS. 35A-37C  are faceted to provide self-illumination with a rounded spheroidal crown that creates a focal point at or near the base of the pavilion. In some embodiments, the first (“mother”) gemstones shown in  FIGS. 35A-37C  are faceted to provide self-illumination with a rounded spheroidal crown that creates a focal point at or near the base of the pavilion, and the second (“daughter”) gemstones may be conventional round brilliant gemstones or other gemstones that may have any other gem cut. 
       FIGS. 38A-38C  illustrate views of an arrangement of a spheroidal faceted gemstone and a heart-shaped gemstone according to an embodiment of the disclosure, where  FIG. 38A  is a top view,  FIG. 38B  is a side view, and  FIG. 38C  is a bottom view. As shown, a first gemstone  3802  (“mother”) is coaxially aligned along axis  3806  with a second gemstone  3804  (“daughter”), such that the light axis of the first first gemstone  3802  is the same as the light axis of the second first gemstone  3804 , i.e., light axis  3806 . The first gemstone  3802  is arranged above the second gemstone  3804  relative to the direction  3808  of incident light towards the gemstone arrangement. In one embodiment, the first gemstone  3802  and the second gemstone  3804  are made from the same gem material. In other embodiments, the first gemstone  3802  and the second gemstone  3804  are made from different gem materials. The reflected light from the second gemstone  3804  then augments illumination, sparkle, and/or body color into the first gemstone  3802 . 
     In various embodiments, in mother-daughter pairs with coaxial alignment, one arrangement for the bottom of the pavilion of the mother is to have a slightly rounded base made up of flat facets and the daughter has a sharp point base. Such an arrangement allows a free exchange of illumination from the mother to the daughter gemstone, yet good reflection from the daughter gemstone. 
     In some embodiments, two or more “daughter” gemstones can be provided in an arrangement with a single “mother” gemstone, as shown in  FIGS. 39A-39C . 
       FIGS. 39A-39C  illustrate views of an arrangement of three spheroidal faceted gemstones according to an embodiment of the disclosure, where  FIG. 39A  is a top view,  FIG. 39B  is a side view, and  FIG. 39C  is a bottom view. As shown, a first gemstone  3902  (“mother”) has light axis  3910 . Two additional gemstones  3904 A,  3904 B (“daughter” gemstones) are included in the arrangement. Gemstone  3904 B is aligned along a light axis  3908  that is perpendicular to the light axis  3910  of the first gemstone  3902  (“mother”). Gemstone  3904 A is aligned along a light axis  3906  that is at a 45° angle relative to a light axis  3910  of the first gemstone  3902  (“mother”). 
     In one embodiment, the first gemstone  3902  and the second gemstones  3904 A,  3904 B are made from the same gem material. In other embodiments, the first gemstone  3902  and the second gemstones  3904 A,  3904 B can be made from different gem materials. 
     When incident light enters the arrangement along direction of light axis  3906 , incident light interacts with the first gemstone  3902 , then the light interacts with the second gemstone  3904 A and reflects from a focal point within the second gemstone  3904 A. The reflected light from the focal point within the second gemstone  3904 A then augments illumination in the first gemstone  3902 . 
     When incident light enters the arrangement along direction of light axis  3908 B, incident light interacts with the first gemstone  3902 , then the light interacts with the second gemstone  3904 B and reflects from a focal point within the second gemstone  3904 B. The reflected light from the focal point within the second gemstone  3904 B then augments illumination in the first gemstone  3902 . 
     In various embodiments, potential daughter gem materials include minerals (e.g., precious fire or jelly, black opal). Also, in some embodiments, the daughter gemstones may include ornamental features, such as letters, numbers, symbols, animals, birds etc., which may be etched into the gem materials. Upon illumination of the daughter gemstone, the ornamental features can be transferred into and optically replicated one or more times in the larger mother gemstone. 
     One example arrangement provides body color suffusion and other optic illumination and gem feature transformation along coaxial light axe. A 5 mm diameter round brilliant faceted daughter cubic zirconia gemstone with canary yellow body color can be coaxially arranged below a 15 mm diameter mother transparent focal point brilliant (e.g., focal point-creating) glass gemstone. Upon illumination, the daughter cubic zirconia transfers its gem brightness, color, brilliance, and sparkle into and completely engulfs the mother gemstone, causing the effect of a 9-fold size increase of the canary yellow cubic zirconia gemstone. 
     Two or more gemstones can be arranged in a jewelry piece in a variety of ways, including in pendants, broaches, bracelets, and rings, for example. 
       FIGS. 40A-40D  illustrate various examples of multiple spheroidal faceted gemstones in a pendant according to various embodiments of the disclosure. 
       FIGS. 41A-41C  illustrate views of multiple spheroidal faceted gemstones in a pendent or broach according to one embodiment of the disclosure, where  FIG. 41A  is a top view,  FIG. 41B  is a side view, and  FIG. 41C  is a bottom view. As shown, the diamond-shaped jewelry piece includes a central gemstone  4102  (“mother”) and a plurality of “daughter” gemstones, including four gemstones  4104  arranged above an opaque surface  4110  of the pendent or broach. A fifth daughter gemstone  4108  is located below the opaque surface  4110 , which also includes a hole  4112  to allow light to reach the gemstone  4108 . In one implementation, a rounded cup (e.g., made from gold or other material)  4114  may secure the gemstone  4108  in the pendent or broach. 
       FIGS. 42A-42D  illustrate various examples of multiple spheroidal faceted gemstones in a pendant or broach according to various embodiments of the disclosure.  FIG. 42A  includes a mother gemstone  4202  and two daughter gemstones  4204 .  FIG. 42B  includes a mother gemstone  4206  and four daughter gemstones  4208 .  FIG. 42C  includes a mother gemstone  4210  and five daughter gemstones, including four daughter gemstones  4212  above an opaque surface and one daughter gemstone  4214  below the opaque surface.  FIG. 42D  includes a mother gemstone  4216  and nine daughter gemstones, including eight daughter gemstones  4218  above an opaque surface and one daughter gemstone  4220  below the opaque surface. 
     According to various embodiments, the mother-daughter gemstones may rest on or against each other, or may be separated by a small distance (e.g., to avoid chipping). In some embodiments, metal prongs may secure the gemstones to the jewelry piece. The metal prongs of each gemstone&#39;s restraint may be secured to the ring, pendant, brooch, or gem cluster structure such that there is a free path of illumination, if possible, between mother(s) and daughter(s) for optical transfer of light, color, and other gem features between the gemstones. Various methods for affixing the gemstones in the jewelry piece are within the scope of the disclosure and can be determined on a case-by-case basis. 
     All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein. 
     The use of the terms “a” and “an” and “the” and “at least one” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The use of the term “at least one” followed by a list of one or more items (for example, “at least one of A and B”) is to be construed to mean one item selected from the listed items (A or B) or any combination of two or more of the listed items (A and B), unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better understand the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention. 
     Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.