Abstract:
The present invention makes use of the spherical sectors, semi-spheres, cylindrical or circular sections of a solid object or the surface of an object, and breaks them into components. If no such spherical sectors, semi-spheres, cylindrical or circular sections are available on the object, or the existing ones cannot be used for any reason, one can create some adequate ones under allowable circumstances. The puzzle will come into being when any of its broken down components can be shared with (interchanged with components of) other flat or spherical or circular or cylindrical surfaces. The idea of the present invention is rather simple, however it may be applied in a versatile manner.

Description:
[0001]     The present invention pertains to a 3-dimensional puzzle, and a way to turn the whole or part of a solid object or the surface of such an object into a 3-dimensional puzzle.  
       BACKGROUND OF THE INVENTION  
       [0002]     Movable-piece type puzzles are known in the prior art. The most famous of these is probably the Rubik&#39;s Cube, which, in its original form, provided a cube with six sides, each side being divided into nine pieces. Eight of the nine pieces may be moved in a sliding fashion such that different colors (or printed indicia, or the like) may be aligned to solve the puzzle.  
         [0003]     The puzzle of the type discussed here is of the kind that certain or all of its components can be moved to other positions within the physical constraints of the puzzle. There are three basic conditions to satisfy. First, every movement must involve more than one component. Second, the components must be moved according to the constraints established in the puzzle. Third, when the components are at the proper positions, there must be more than one “route” available for each movable component.  
         [0004]     The object of the game is to array the components to some desired patterns or get the original overall shape back from the disordered condition. The following are two examples of this type of puzzle.  
         [0005]     In the first example, if the components are, say, some color surfaces or alphabets, or the like, the player can make some color patterns or words from the available alphabets, or would be under some rules established by the players themselves to finish the specified color patterns or words within a time frame.  
         [0006]     In a second example, if the components are some printed graphics, animated or contoured patterns, the player is to find a way to move all the components back to their original interrelated locations from their dislocated positions.  
         [0007]     Such puzzles have proved to be popular, and other shapes and sizes of such puzzles have been designed. Examples of such puzzles include, but are not limited to, the puzzles disclosed in the following patents, all of which are incorporated herein by reference:  
                                                   Patent No.   Inventor                            D190,660   Mote           6,626,431   Possidento           6,120,356   Li           5,992,850   Li           5,826,871   Li           5,271,688   Chang           4,706,956   Abu-Shumays et al.           4,593,907   Abu-Shumays et al.           4,586,713   Abu-Shumays et al.           4,558,866   Alford           4,540,177   Horvath           4,478,418   Sherman, Jr.           4,474,377   Ashley           4,453,715   Halpern           4,451,039   Hewlett, Jr.           4,427,197   Doose           4,421,311   Sebesteny           4,415,158   Engel           4,405,131   Horvath           4,378,117   Rubik           4,378,116   Rubik           4,344,623   Isobe           3,690,672   Dreyer           3,655,194   Pierson           3,081,089   Gustafson             636,109   Bowers                      
 
       SUMMARY OF THE INVENTION  
       [0008]     In the present invention, a method is provided to generate an N×N×N element puzzle, (where N refers to any positive integer) of the Rubik&#39;s Cube variety, but not limited to the shape of a cube. The puzzle of the present invention can be used to create many numbers of puzzle designs as illustrated herein.  
         [0009]     The present invention makes use of the spherical sectors, semi-spheres, cylindrical or circular sections of a solid object or the surface of an object, and breaks them into components. If no such spherical sectors, semi-spheres, cylindrical or circular sections are available on the object, or the existing ones cannot be used for any reason, one can create some adequate ones under allowable circumstances. The puzzle will come into being when any of the sectors or its broken down components can be shared with (interchanged with components of) other flat or spherical or circular or cylindrical surfaces. The idea of the present invention is rather simple, however it can be applied with versatility.  
         [0010]     According to a first aspect of the present invention, there is provided a three-dimensional sliding element puzzle comprising a core member having at least one circular or annular cross-section; and a plurality of puzzle members engageable with each other and slidably movable on an outer surface of said core member at least about a longitudinal axis of said cross section; wherein at least one said puzzle member is selectively movable relative to another said puzzle member along at least two different paths; and wherein said puzzle members are inter-engaged with each other for relative sliding movement.  
         [0011]     According to a second aspect of the present invention, there is provided a three-dimensional sliding element puzzle comprising a core member having at least one circular or annular cross-section; a plurality of puzzle members slidably movable on an outer surface of said core member; and a plurality of peg members engaged with said outer surface of said core member, each said peg member having an outer part and an inner part; wherein said plurality of puzzle members are engageable with each other and/or with at least one said peg member for relative movement; wherein at least one said puzzle member is selectively movable relative to another said puzzle member along at least two different paths; wherein at least one said puzzle member has an outer part and an inner part; and wherein said inner part of said puzzle member is in contact with at least one peg member.  
         [0012]     According to a third aspect of the present invention, there is provided a three-dimensional sliding element puzzle comprising a core member having at least one circular or annular cross-section; a plurality of puzzle members slidably movable on an outer surface of said core member; and a plurality of peg members engaged on said outer surface of said core member; wherein said plurality of puzzle members are engageable with each other and/or with said peg members for relative movement; wherein at least one said puzzle member is selectively movable relative to another said puzzle member along at least two different paths; and wherein said peg members and said puzzle members are inter-engaged with each other directly or indirectly for relative sliding movement. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0013]     Preferred embodiments of the present invention will now be described, by way of examples only, with reference to the accompanying drawings, in which:  
         [0014]      FIGS. 1A  to  1 D show, respectively, a top view, a side view, a front view, and a perspective view, of an arcuate puzzle segment made up of one generally square component and four edge fillers.  
         [0015]      FIGS. 2A  to  2 D show, respectively, a top view, a side view, a front view, and a perspective view of a sphere formed of six of the segments of  FIG. 1D , with the edge fillers shared by adjacent segments.  
         [0016]      FIGS. 3A  to  3 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment derived from that shown in  FIG. 1D .  
         [0017]      FIGS. 3E  to  3 H show, respectively, an exploded top view, an exploded side view, an exploded front view, and an exploded perspective view, of the segment shown in  FIG. 3D .  
         [0018]      FIGS. 4A  to  4 D show, respectively, a top view, a side view, a front view, and a perspective view of a sphere formed of six of the segments of  FIG. 3D , with the edge fillers shared by adjacent segments.  
         [0019]      FIGS. 5A  to  5 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of one generally pentagon component and five edge fillers.  
         [0020]      FIGS. 6A  to  6 C show, respectively, a top view, a side view, and a front view, of a sphere formed of twelve of the segments shown in  FIG. 5D , with the edge fillers shared by adjacent segments.  
         [0021]      FIGS. 7A  to  7 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment derived from that shown in  FIG. 5D .  
         [0022]      FIGS. 8A  to  8 C show, respectively, a top view, a side view, and a front view of a sphere formed of twelve of the segments of  FIG. 7D , with the edge fillers shared by adjacent segments.  
         [0023]      FIGS. 9A  to  9 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of one generally triangular component, three big edge fillers and three small edge fillers.  
         [0024]      FIGS. 9E  to  9 G show, respectively, an exploded top view, an exploded side view, and an exploded front view, of the segment shown in  FIG. 9D .  
         [0025]      FIGS. 10A  to  10 C show, respectively, a top view, a side view, and a front view of a sphere formed of four of the segments of  FIG. 9D , with the edge fillers shared by adjacent segments.  
         [0026]      FIGS. 11A  to  11 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment derived from that shown in  FIG. 9D .  
         [0027]      FIGS. 12A  to  12 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of one generally triangular component and three edge fillers, forming part of the segment shown in  FIG. 11D .  
         [0028]      FIGS. 13A  to  13 C show, respectively, a top view, a side view, and a front view of a sphere formed of four of the segments of  FIG. 11D , with the edge fillers shared by adjacent segments.  
         [0029]      FIGS. 14A  to  14 D show respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment, which may be used for forming the sphere of  FIG. 13A  with an arcuate segment of  FIG. 11D .  
         [0030]      FIGS. 15A  to  15 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of five generally triangular components and ten edge fillers.  
         [0031]      FIGS. 16A  to  16 C show, respectively, a top view, a side view, and a front view of a sphere made up of twelve of the segments of  FIG. 15D , with the edge fillers shared by adjacent segments.  
         [0032]      FIGS. 17A  to  17 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment derived from the sector of  FIG. 15D .  
         [0033]      FIGS. 18A  to  18 D show, respectively, a top view, a side view, a front view, and a perspective view of a further arcuate puzzle segment derived from the segment of  FIG. 15D .  
         [0034]      FIGS. 19A  to  19 C show, respectively, a top view, a side view, and a front view, of a sphere made of twelve of the segments of  FIG. 17D , with the edge fillers shared by adjacent segments.  
         [0035]      FIGS. 20A  to  20 C show, respectively, a top view, a side view, and a front view, of a sphere made of twelve of the segments of  FIG. 18D , with the edge fillers shared by adjacent segments.  
         [0036]      FIGS. 21A  to  21 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment derived from the segment of  FIG. 17D .  
         [0037]      FIGS. 22A  to  22 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment derived from the segment of  FIG. 18D .  
         [0038]      FIGS. 23A  to  23 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of one pentagonal component, five triangular fillers and five inter-fillers.  
         [0039]      FIGS. 23E  to  23 H show, respectively, an exploded top view, an exploded side view, an exploded front view, and an exploded perspective view of the segment shown in  FIG. 23D .  
         [0040]      FIGS. 24A  to  24 C show, respectively, a top view, a side view, and a front view, of a sphere formed of twelve of the segments of  FIG. 23D , with the fillers shared by adjacent segments.  
         [0041]      FIGS. 25A  to  25 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of one triangular component, nine small fillers and three edge fillers.  
         [0042]      FIGS. 26A  to  26 C show, respectively, a top view, a side view, and a front view, of a sphere formed of twenty of the segments of  FIG. 25D , with the fillers shared by adjacent segments.  
         [0043]      FIGS. 27A  to  27 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment of twenty-seven components.  
         [0044]      FIGS. 28A  to  28 C show, respectively, a top view, a side view, and a front view, of a sphere formed of twenty of the segments of  FIG. 27D .  
         [0045]      FIGS. 29A  to  29 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of one pentagonal component and five edge fillers.  
         [0046]      FIGS. 30A  to  30 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate puzzle segment made up of one hexagonal component and six edge fillers.  
         [0047]      FIGS. 31A  to  31 C show, respectively, a top view, a side view, and a front view of a sphere made of twelve of the segments of  FIG. 29D  and twenty of the segments of  FIG. 30D , with the edge fillers shared by adjacent segments.  
         [0048]      FIGS. 32A  to  32 D show, respectively, a top view, a side view, a front view, and a perspective view of a further arcuate puzzle segment design.  
         [0049]      FIGS. 33A  to  33 D show, respectively, a top view, a side view, a front view, and a perspective view of another arcuate puzzle segment design.  
         [0050]      FIGS. 34A  to  34 D show, respectively, a top view, a side view, a front view, and a perspective view of a sphere, which may be made up of six of the segments of  FIG. 32D  or eight of the segments of  FIG. 33D , with the fillers shared by adjacent segments.  
         [0051]      FIGS. 35A  to  35 D show, respectively, a top view, a side view, a front view, and a perspective view of a hemisphere, two of which may be combined to form the sphere of  FIG. 34D .  
         [0052]      FIGS. 36A  to  36 D show, respectively, a top view, a side view, a front view, and a perspective view of a hemisphere made up of four semi-segments.  
         [0053]      FIGS. 37A  to  37 D show, respectively, a top view, a side view, a front view, and a perspective view of a sphere made up of two of the hemispheres of  FIG. 36D .  
         [0054]      FIGS. 38A  to  38 D show, respectively, a top view, a side view, a front view, and a perspective view of a further arcuate puzzle segment.  
         [0055]      FIGS. 38E  to  38 H show, respectively, an exploded top view, an exploded side view, an exploded front view, and an exploded perspective view of the segment shown in  FIG. 38D .  
         [0056]      FIGS. 39A  to  39 D show, respectively, a top view, a side view, a front view, and a perspective view of a cylindrical ring conforming to the profile of the segment of  FIG. 38D .  
         [0057]      FIGS. 40A  to  40 D show, respectively, a top view, a side view, a front view, and a perspective view of a further cylindrical ring conforming to the profile of the segment of  FIG. 38D .  
         [0058]      FIGS. 41A  to  41 D show, respectively, a front view, a side view, a top view and a perspective view of a vessel, the puzzle part of which being formed of fifteen of the arcuate puzzle segments of  FIG. 38D  or two of the cylindrical rings of  FIG. 39D  and one cylindrical ring of  FIG. 40D .  
         [0059]      FIG. 42A  to  42 D show, respectively, a top view, a side view, a front view, and a perspective view of a cylindrical ring, which may be placed around the puzzle of  FIG. 39D  so that the subassembly may be turned on the vessel of  FIG. 41D .  
         [0060]      FIGS. 43A  to  43 C show, respectively, a top view, a side view, and a front view of a sub-assembly formed by two conjoining two arcuate puzzle segments with each other.  
         [0061]      FIG. 44  shows a ring, which may be formed of eight of the sub-assembly of  FIG. 43A .  
         [0062]      FIGS. 45A  to  45 D show, respectively, a top view, a side view, a front view, and a perspective view of a ball with flutes made for receiving the rings of  FIG. 44  for relative sliding movement.  
         [0063]      FIGS. 46A  to  46 D show, respectively, a top view, a side view, a front view, and a perspective view of a puzzle formed of three of the rings of  FIG. 44  joined together in an orthogonal manner and the ball of  FIG. 45D .  
         [0064]      FIGS. 47A  to  47 D show, respectively, a top view, a side view, a front view, and a perspective view of a cylindrical ring.  
         [0065]      FIGS. 48A  to  48 D show, respectively, a top view, a side view, a front view, and a perspective view of a sector of a cylindrical column.  
         [0066]      FIGS. 49A  to  49 C show, respectively, a top view, a side view, and a perspective view of a cup, the puzzle part of which being formed of ten of the cylindrical rings of  FIG. 47D  or twenty of the cylindrical column sectors of  FIG. 48D .  
         [0067]      FIGS. 50A  to  50 D show, respectively, a top view, a side view, a front view, and a perspective view of a cylindrical ring.  
         [0068]      FIGS. 51A  to  51 D show, respectively, a top view, a side view, a front view, and a perspective view of a ⅙ segment.  
         [0069]      FIGS. 52A  to  52 D show, respectively, a top view, a side view, a front view, and a perspective view of a 1/12 segment.  
         [0070]      FIGS. 53A  to  53 D show, respectively, a top view, a side view, a front view, and a perspective view of a container with a puzzle.  
         [0071]      FIGS. 54A  to  54 D show, respectively, a top view, a side view, a front view, and a perspective view of a puzzle, being a combination of two of the puzzle parts of the container in  FIGS. 53A  to  53 D.  
         [0072]      FIGS. 55A  to  55 D show, respectively, a top view, a side view, a front view, and a perspective view of a puzzle component.  
         [0073]      FIGS. 56A  to  56 D show a core body relative to which the puzzle component shown in  FIGS. 55A  to  55 D is movable.  
         [0074]      FIGS. 57A  to  57 D show, respectively, a top view, a side view, a front view, and a perspective view of a bare puzzle.  
         [0075]      FIGS. 58A  to  58 D show, respectively, a top view, a side view, a front view and a perspective view of a sphere generated from a cube.  
         [0076]      FIGS. 59A  to  59 C show, respectively, a top view, a side view, and a front view of a sphere generated from a dodecahedron.  
         [0077]      FIGS. 60A  to  60 C show, respectively, a top view, a side view, and a front view of a sphere generated from an icosahedron.  
         [0078]      FIGS. 61A  to  61 C show, respectively, a top view, a side view, and a front view of a sphere generated from a tetrahedron.  
         [0079]      FIGS. 62A  to  62 C show, respectively, a top view, a side view, and a front view of a sphere generated from a 32-facet “soccer ball”.  
         [0080]      FIGS. 63A  to  63 D show, respectively, a top view, a side view, a front view, and a perspective view of an arcuate square segment cut by a flat cutting plane.  
         [0081]      FIGS. 64A  to  64 D show, respectively, a top view, a side view, a front view, and a perspective view of a sphere formed of six of the segments shown in  FIG. 63D , with the obstructions cleared.  
         [0082]      FIGS. 65A  to  65 D show, respectively, a top view, a side view, a front view, and a perspective view of a cone-shape cutting plane cutting one of the sides of two arcuate segments at the same time.  
         [0083]      FIGS. 66A  to  66 D show, respectively, a top view, a side view, a front view, and a perspective view of a sphere with the obstructions cleared.  
         [0084]      FIGS. 67A and 67D  are respectively a top view and a perspective view of a reversed cone-shape cutting plane cutting two arcuate segments at the same time.  
         [0085]      FIG. 67B  is a sectional view taken along the line B-B of  FIG. 67A .  
         [0086]      FIG. 67C  is a sectional view taken along the line C-C of  FIG. 67A .  
         [0087]      FIGS. 68A  to  68 D show, respectively, a top view, a side view, a front view, and a perspective view of a sphere with the obstructions cleared by the cone-shaped cutting plane of  FIG. 67D .  
         [0088]      FIGS. 69A and 69B  show, respectively, a top view and a side view of a first method in which cylindrical cutting planes cut out a puzzle component.  
         [0089]      FIGS. 69C and 69D  show, respectively, a top view and a side view of the component cut out by the arrangement in  FIGS. 69A and 69B .  
         [0090]      FIGS. 70A and 70B  show, respectively, a top view and a side view of a second method in which cylindrical cutting planes cut out a puzzle component.  
         [0091]      FIGS. 70C and 70D  show, respectively, a top view and a side view of the component cut out by the arrangement in  FIGS. 70A and 70B .  
         [0092]      FIGS. 71A and 71B  show, respectively, a top view and a side view of a third method in which cylindrical cutting planes cut out a puzzle component.  
         [0093]      FIGS. 71C and 71D  show, respectively, a top view and a side view of the puzzle component cut out by the arrangement in  FIGS. 71A and 71B .  
         [0094]      FIGS. 72A and 72B  show, respectively, a top view and a front view of a fourth method in which cylindrical cutting planes cut out a puzzle component.  
         [0095]      FIGS. 72C and 72D  show, respectively, a top view and a front view of the puzzle component cut out by the arrangement in  FIGS. 72A and 72B .  
         [0096]      FIGS. 73A and 73B  show, respectively, a top view and a front view of a fifth method in which cylindrical cutting planes cut out a component.  
         [0097]      FIGS. 73C and 73D  show, respectively, a top view and a front view of the puzzle component cut out by the arrangement in  FIGS. 73A and 73B .  
         [0098]      FIGS. 74A  to  74 C show, respectively, a top view, a side view, and a front view of a sphere assembled with the three components of FIGS.  69 C-D, FIGS.  70 C-D and  71 C-D, and FIGS.  72 C-D and  73 C-D.  
         [0099]      FIGS. 75A  to  75 C show, respectively, a top view, a front view, and a side view of an arcuate puzzle segment.  
         [0100]      FIG. 75D  shows a vertex view of a sphere formed of a number of the sectors shown in  FIG. 75A -C.  
         [0101]      FIG. 76A  to  76 C show, respectively, a top view, a front view, and a side view of a further arcuate puzzle segment.  
         [0102]      FIG. 76D  shows a vertex view of a sphere formed of a number of the segments shown in  FIG. 76A -C.  
         [0103]      FIGS. 77A  to  77 C show, respectively, an exploded top view, an exploded side view, and an exploded front view, of a few components in one embodiment of the present invention.  
         [0104]      FIGS. 78A  to  78 D show, respectively, a top view, a front view, a side view, and a perspective view of a sphere built with the components shown in FIGS.  77 A-C, but with one of the arcuate puzzle segments removed for showing the inner ball.  
         [0105]      FIGS. 79A  to  79 C are, respectively, a top view, a side view, and a front view of the triangular puzzle component in FIGS.  77 A-C.  
         [0106]      FIGS. 80A  to  80 C are, respectively, a top view, a side view, and a front view of the filler in FIGS.  77 A-C.  
         [0107]      FIGS. 81A  to  81 D show, respectively, a top view, a side view, a front view, and a perspective view of a component, forming part of the cylinder ring in FIGS.  47 A-D, and of the cylinder column in FIGS.  48 A-D.  
         [0108]      FIGS. 82A  to  82 D show, respectively, a top view, a side view, a front view, and a perspective view of a spring disc, being an additional component of the sphere shown in FIGS.  16 A-C.  
         [0109]      FIGS. 83A  to  83 D show, respectively, a top view, a side view, a front view, and a perspective view of a peg, being a further additional component of the sphere of  FIG. 16A -C.  
         [0110]      FIG. 84  shows an inner ball assembled with a number of the spring discs of FIGS.  82 A-D and a number of the pegs of FIGS.  83 A-D.  
         [0111]      FIG. 85  shows the actual pegs in the assembly.  
         [0112]      FIG. 86  shows the sub-assembly after a number of triangular puzzle components are assembled on the spring discs.  
         [0113]      FIGS. 87A  to  87 D show, respectively, a top view, a side view, a front view, and a perspective view of a skeleton.  
         [0114]      FIGS. 88A  to  88 D show, respectively, an exploded top view, an exploded side view, an exploded front view, and an exploded perspective view of the skeleton of  FIGS. 87A-87D  with components of the spherical sector of  FIGS. 9A-9G   
         [0115]      FIGS. 89A  to  89 D show, respectively, a top view, a side view, a front view, and a perspective view of a first half of the assembly of FIGS.  91 A-D.  
         [0116]      FIGS. 90A  to  90 D show, respectively, a top view, a side view, a front view, and a perspective view of a second half of the assembly of FIGS.  91 A-D.  
         [0117]      FIGS. 91A  to  91 D show, respectively, a top view, a side view, a front view, and a perspective view of a puzzle assembly, which is basically a sphere modified to an odd object formed from either two of the halves of FIGS.  89 A-D or two of the halves of FIGS.  90 A-D.  
         [0118]      FIG. 92A  shows a perspective view of a puzzle assembly based on the sphere of FIGS.  37 A-D, having been modified to a long rod.  
         [0119]      FIGS. 92B and 92C  are two respective views showing the rod in  FIG. 92A  turned about a plane.  
         [0120]      FIGS. 93A  to  93 D show, respectively, a top view, a side view, a front view, and a perspective view of a cylindrical ring of sixteen tiles.  
         [0121]      FIGS. 94A  to  94 D show, respectively, a top view, a side view, a front view, and a perspective view of three of the rings of FIGS.  93 A-D being joined together in an orthogonal manner to form a puzzle with an inner ball.  
         [0122]      FIGS. 95A  to  95 D show, respectively, a top view, a side view, a front view, and a perspective view of the rings in Figs. FIGS.  94 A-D.  
         [0123]      FIGS. 96A  to  96 D show, respectively, a top view, a side view, a front view, and a perspective view of the inner ball of FIGS.  94 A-D.  
         [0124]      FIGS. 97A  to  97 D show, respectively, a top view, a side view, a front view, and a perspective view of a square peg.  
         [0125]      FIGS. 98A and 98C  show, respectively, a front view and a bottom view of an arcuate puzzle segment, being 1/8th of a sphere.  
         [0126]      FIG. 98B  is a sectional view taken along line D-D in  FIG. 98A .  
         [0127]      FIG. 98D  is a perspective view of the spherical shell in  FIG. 98A .  
         [0128]      FIG. 99  shows six poles of the pegs of  FIGS. 97A-97D  and eight inner triangles of the shells of FIGS.  98 A-D assembled on the inner ball, with the top layers of the pegs and the spherical shell segments hidden to reveal the assembly.  
         [0129]      FIG. 100  shows the actual pegs in the assembly.  
         [0130]      FIG. 101A  is a front view of the complete sphere shown in  FIG. 100 .  
         [0131]      FIG. 101B  is a sectional view taken along the line E-E in  FIG. 101A .  
         [0132]      FIGS. 102A  to  120 D show, respectively, a top view, a side view, a perspective view, and a bottom of a triangular peg.  
         [0133]      FIGS. 103A  to  103 C show, respectively, a top view, a side view, and a front view of an arcuate segment, being 1/8th of a sphere.  
         [0134]      FIG. 104  shows a sphere assembled with a number of the triangular pegs of FIGS.  102 A-C and a number of the internal portion of the arcuate shell segment of FIGS.  103 A-C.  
         [0135]      FIGS. 105A and 105B  show two perspective views of an inner ball assembled to the sphere of  FIG. 104 , but with four arcuate shell segments of FIGS.  103 A-C hidden.  
         [0136]      FIG. 106A  shows an arcuate puzzle segment, being 1/6th of a sphere.  
         [0137]      FIG. 106B  shows a rail for holding adjacent arcuate shell segments together.  
         [0138]      FIG. 106C  shows a hexagonal peg.  
         [0139]      FIG. 107A  shows an assembled sphere.  
         [0140]      FIG. 107B  shows the sphere in  FIG. 107A  with the top layers of the arcuate shell segments hidden to reveal the inside.  
         [0141]      FIG. 108A  shows the sphere in  FIG. 107B  with the pegs and rails removed.  
         [0142]      FIG. 108B  shows the “naked” pegs and “naked” rails put back onto the sphere, with the top layers of the pegs and rails hidden to reveal the structure underneath.  
         [0143]      FIG. 109A  shows a peg.  
         [0144]      FIG. 109B  shows an arcuate shell segment, being 1/6th of a sphere.  
         [0145]      FIG. 110A  shows an assembled sphere.  
         [0146]      FIG. 110B  shows the sphere in  FIG. 110A , but with the top layers of the arcuate segment shell segments hidden to reveal the inside.  
         [0147]      FIG. 111A  shows the sphere of  FIG. 110A  with half of the arcuate segment shells removed.  
         [0148]      FIG. 111B  shows the sphere of  FIG. 111A , in which both the top layers of the arcuate shell segments and the pegs are hidden to reveal the structure underneath.  
         [0149]      FIGS. 112A  to  112 F show various views of an arcuate shell segment, being 1/4th of a hemisphere.  
         [0150]      FIG. 113  shows a peg.  
         [0151]      FIG. 114  shows the use of three of the pegs of  FIG. 113  to keep a number of the arcuate shell segments of FIGS.  112 A-F on an inner ball.  
         [0152]      FIG. 115  shows an arrangement alternative to that shown in  FIG. 114 , with additional pegs.  
         [0153]      FIG. 116  shows yet a further alternative arrangement in which the additional pegs are replaced by rails.  
         [0154]      FIG. 117A  shows the use of square pegs, in place of those shown in  FIG. 115 .  
         [0155]      FIG. 117B  shows a square peg as used in the puzzle in  FIG. 117A .  
         [0156]      FIG. 118  shows the use of square pegs.  
         [0157]      FIG. 119A  shows an arcuate segment shell, being of a 1/4th of a hemisphere.  
         [0158]      FIG. 119B  shows a peg.  
         [0159]      FIG. 120  shows a puzzle using a number of the pegs in  FIG. 119B .  
         [0160]      FIG. 121  shows a further puzzle using a number of the pegs in  FIG. 119B .  
         [0161]      FIG. 122A  shows a puzzle similar to that shown in  FIG. 120 , with the space between the pegs filled with rails.  
         [0162]      FIG. 122B  shows a rail used in the puzzle in  FIG. 122A .  
         [0163]      FIGS. 123A  to  123 E show various views of an arcuate segment shell, being 1/4th of a hemisphere.  
         [0164]      FIG. 124A  shows a ball assembly with an inner ball mounted with a number of pegs and rails, with four of the arcuate segment shells removed to show the inner details.  
         [0165]      FIG. 124B  shows a peg.  
         [0166]      FIG. 124C  shows a rail.  
         [0167]      FIG. 125A  to  125 E show various views of a segment of an arcuate segment shell, being in the form of 1/4th of a hemisphere.  
         [0168]      FIG. 126A  shows a ball assembly with an inner ball mounted with a number of pegs and rails, with three of the spherical shell segments removed to show the inner details.  
         [0169]      FIGS. 126B and 126D  show two perspective views of the peg in  FIG. 126A ,  
         [0170]      FIG. 126C  shows the rail in  FIG. 126A .  
         [0171]      FIG. 127A  shows a ball assembly with an inner ball mounted with a number of pegs and rails, with three of the spherical shell segments removed to show the inner details.  
         [0172]      FIG. 127B  shows a peg used in the assembly of  FIG. 127A .  
         [0173]      FIG. 127C  shows a rail used in the assembly of  FIG. 127A .  
         [0174]      FIG. 127D  shows a spherical shell segment used in the assembly of  FIG. 127A .  
         [0175]      FIG. 128A  shows a rail with a raised rib.  
         [0176]      FIG. 128B  to  128 D show various views of a peg with a post.  
         [0177]      FIGS. 129A and 129B  show a puzzle globe using a number of the rails of  FIG. 128A  and a number of the pegs of  FIG. 128B -C.  
         [0178]      FIGS. 130 and 131 A-C show various views of a further puzzle globe formed of a number of the rails of  FIG. 128A  and a number of the pegs of  FIG. 128B -D.  
         [0179]      FIG. 132A  to  132 D show various views of a yet further globe puzzle using a number of the rails of  FIG. 128A  and a number of the pegs of  FIG. 128B -D, with the posts of the pegs and ribs of the rails widened and not raised.  
         [0180]      FIG. 133A  shows a fluted inner ball  
         [0181]      FIG. 133B  shows an arcuate puzzle segment, being in the form of 1/6th of a sphere.  
         [0182]      FIG. 134A  shows an assembled sphere formed of the inner ball of  FIG. 133A  and a number of the segments of  FIG. 133B .  
         [0183]      FIG. 134B  shows the same sphere as shown in  FIG. 134A , but with the top layers of the arcuate segment shells hidden to reveal their pegs trapped by inside the undercut flutes.  
         [0184]      FIG. 135A  shows an inner ball pre-assembled with six pegs about the equatorial region.  
         [0185]      FIG. 135B  shows a fluted arcuate puzzle segment, being in the form of 1/6th of a sphere.  
         [0186]      FIG. 136A  shows an assembled sphere formed of the inner ball of  FIG. 135A  and five of the segments of  FIG. 135B .  
         [0187]      FIG. 136B  shows the same assembled sphere of  FIG. 136A , with the top layers of the arcuate shell segments hidden to reveal the interior structure.  
         [0188]      FIGS. 137A  to  137 D show various views of a vessel modified from the puzzle design of  FIG. 10A -C.  
         [0189]      FIGS. 138A  to  138 D show various views of a vessel modified from the spherical sector of  FIG. 14A -D.  
         [0190]      FIGS. 139A  to  139 D show various views of a vessel modified from the puzzle design of FIGS.  24 A-C.  
         [0191]      FIGS. 140A  to  140 D show various views of a vessel modified and simplified from the puzzle globe of FIGS.  34 A-D.  
         [0192]      FIG. 141A  to  141 D show various views of a puzzle based on the puzzle of FIGS.  2 A-D, but with the cutting planes altered.  
         [0193]      FIGS. 142A  to  142 F show various views of a puzzle globe based on the puzzle globe of FIGS.  10 A-C with different cutting planes.  
         [0194]      FIGS. 143A  to  143 D show various views of a puzzle based on the puzzle globe of FIGS.  142 A-F, which is in turn based on the puzzle globe of FIGS.  10 A-C with different cutting planes.  
         [0195]      FIGS. 144A  to  144 D show a puzzle generated from the puzzle globe of FIGS.  10 A-C, with the positions of the cutting planes adjusted.  
         [0196]      FIGS. 145A and 145B  show, respectively, an exploded top view and an exploded side view of the puzzle of FIGS.  143 A-D, in which the core puzzle of is the puzzle of FIGS.  142 A-F.  
         [0197]      FIGS. 146A  to  146 C show various views of a puzzle modified on the basis of the puzzle globe of FIGS.  24 A-C.  
         [0198]      FIG. 147  is an exploded view of a further puzzle according to the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0199]      FIGS. 1A  to  1 D show an arcuate puzzle segment  100  made up of one generally square component  102  and four adjacent edge fillers  104 . Six of these segments may combine to form a sphere  200  as shown in  FIGS. 2A  to  2 D. The edge fillers  104  may be common parts shared by adjacent segments  100 . In particular, each of the edge fillers  104  is slidably movable relative to the square component  102  along their respective common surface. It is thus possible to provide graphic or other patterns on the surface of the components  102  and edge fillers  104 , to thereby form a puzzle.  
         [0200]      FIGS. 3A  to  3 H show an arcuate puzzle segment  300 , derived from the segment  100  of  FIGS. 1A  to  1 D. Six of these segments  300  may be used for forming a sphere  400  as shown in  FIGS. 4A  to  4 D. It can be seen that there are interlocking arrangements between the parts forming the segments  300 , which will be discussed in more detail below.  
         [0201]     As noted above, in a Rubik&#39;s Cube, eight puzzle pieces may be moved in a sliding fashion. The piece at the center cannot slide. The three pieces at each side can be viewed as similar to the “edge fillers” of the present invention. Moreover, the puzzle of  FIGS. 4A  to  4 D can be changed to somewhat like a 5×5×5 Rubik&#39;s Cube. However, because the spacing between the “cuts” is not considered for this purpose, the eight corners (vertexes) of the cube may be void. By adjusting the spacing and number of “cuts”, one can make another N×N×N cubic puzzle.  
         [0202]      FIGS. 5A  to  5 D show an arcuate puzzle segment  500  made up of one central pentagonal component  502  and five edge fillers  504 , in which the edge fillers are slidably movable relative to the central component  502  along their respective common surface. Twelve of these segments  500  may be used for forming a puzzle sphere  600  of FIGS.  6 A-C. When forming the sphere  600 , the edge fillers  504  are common parts shared by adjacent spherical segments  500 .  
         [0203]      FIGS. 7A  to  7 D show an arcuate puzzle segment  700  based on that shown in  FIGS. 5A  to  5 D, with the central component  502  and edge fillers  504  further cut to form additional sub-parts. Twelve of these segments  700  may be used for forming a sphere  800  as shown in  FIGS. 8A  to  8 C. When forming the puzzle sphere  800 , all components other than the pentagon  802  at the center of each segment may be common parts shared by adjacent spherical segments  800 .  
         [0204]      FIGS. 9A  to  9 G show various views of an arcuate puzzle segment  900  made up of one central triangular component  902 , three big edge fillers  904  and three small edge fillers  906 , which are slidably movable relative to one another along their respective common surfaces. Four of these segments  900  may be used for forming a puzzle sphere  1000  in  FIGS. 10A  to  10 C. All the edge fillers  904 ,  906  may be common parts shared by adjacent segments  900 , when forming the sphere  1000 .  
         [0205]      FIGS. 11A  to  11 D show various views of an arcuate puzzle segment  1100 , being derived on that shown in  FIGS. 9A  to  9 G The segment  1100  includes another arcuate puzzle segment  1200 , as shown in  FIGS. 12A  to  12 D, which is made up of one central generally triangular component  1202  and three edge fillers  1204 , which are slidably movable relative to the component  1202  along their respective common surface. Four of the segments  1100  may be used for forming a sphere  1300  as shown in FIGS.  13 A-C. On the other hand, the puzzle sphere  1300  may instead be formed with an arcuate puzzle segment  1100  and an arcuate puzzle segment  1400  shown in  FIGS. 14A  to  14 D. If the segment  1400  is considered to be the sector for turning, all components may be common parts shared with by the adjacent segments  1100 ,  1400 . If, on the other hand, the segment  1100  is considered to be the segment for turning, all components other than the triangle at the center of the segment may be common parts shared by adjacent segments  1100 ,  1400 .  
         [0206]      FIGS. 15A  to  15 D show an arcuate puzzle segment  1500  made up of five generally triangular components  1502  and ten edge fillers  1504 . Twelve of these segments  1500  may be combined to form a puzzle sphere  1600  as shown in FIGS.  16 A-C. All components may be common parts shared by adjacent segments  1500  when forming the sphere  1600 .  
         [0207]      FIGS. 17A  to  17 D show various views of an arcuate puzzle segment  1700 , and  FIGS. 18A  to  18 D show various views of an arcuate puzzle segment  1800 , both being derived from the segment  1500  shown in  FIGS. 15A  to  15 D. Twelve of each of the segments  1700 ,  1800  may be used for forming a puzzle sphere  1900  shown in FIGS.  19 A-C, or a puzzle sphere  2000  shown in  FIGS. 20A  to  20 C.  
         [0208]     It can be seen that each of the segments  1700 ,  1800  includes an arcuate puzzle segment  2100  as shown in  FIGS. 21A  to  21 D and an arcuate puzzle segment  2200  as shown in  FIGS. 22A  to  22 D. All components may be common parts shared by adjacent segments when forming the spheres  1900 ,  2000 .  
         [0209]      FIGS. 23A  to  23 H show an arcuate puzzle segment  2300  made up of one central generally pentagonal component  2302 , five generally triangular fillers  2304  and five inter-fillers  2306 , which are slidably movable relative to one another along their respective common surface. Twelve of these segments  2300  may be used for forming a puzzle sphere  2400  of  FIG. 24 . All the triangular fillers  2304  and inter-fillers  2306  may be common parts shared by adjacent segments  2300  when forming the sphere  2400 . It can be seen that the segment  700  shown in FIGS.  7 A-D may be considered to be equivalent to the segment  500  in FIGS.  5 A-D plus the segment  2300  shown in FIGS.  23 A-H.  
         [0210]      FIGS. 25A  to  25 D show various views of an arcuate puzzle segment  2500  made up of one central triangular component  2502 , nine small fillers  2504  and three edge fillers  2506 , which are slidably movable relative to one another along their respective common surface. Twenty of these segments  2500  may be used for forming a sphere  2600  as shown in  FIGS. 26A  to  26 C. All the fillers  2504  and edge fillers  2506  may be common parts shared by adjacent segments  2500 , when forming the puzzle sphere  2600 .  
         [0211]      FIGS. 27A  to  27 D show various views of an arcuate puzzle segment  2700  of twenty-seven components, which are slidably movable relative to each other along their respective common surface. Twenty of these segments  2700  may be used for forming a sphere  2800  as shown in  FIGS. 28A  to  28 C. All components in the sector  2700  may be common parts shared by adjacent segments  2700  when forming the sphere puzzle  2800 .  
         [0212]      FIGS. 29A  to  29 D show various views of an arcuate puzzle segment  2900  made up of one central arcuate pentagonal component  2902  and five edge fillers  2904 . The edge fillers  2904  are slidably movable relative to the central component  2902  along their respective common surface.  FIGS. 30A  to  30 D show various views of an arcuate puzzle segment  3000  made up of one central arcuate hexagonal component  3002  and six edge fillers  3004 . The edge fillers  3004  are slidably movable relative to the central component  3002  along their respective common surface. Twelve segments  2900  and twenty segments  3000  may be used for forming a sphere  3100  as shown in FIGS.  31 A-C. The edge fillers  2904 ,  3004  may be common parts shared by adjacent segments  2900 ,  3000  when forming the sphere puzzle  3100 .  
         [0213]      FIGS. 32A  to  32 D show various views of an arcuate puzzle segment  3200 , and  FIGS. 33A  to  33 D show another arcuate puzzle segment  3300 , each being formed of a number of slidably movable components. Six of the segments  3200  or eight of the segments  3300  may be combined to form a sphere puzzle  3400  as shown  FIGS. 34A  to  34 D. All components other than a big arcuate square component  3202  at the center of the segment  3200 , or a big arcuate triangular component  3302  at the center of the segment  3300  may be common parts shared by adjacent segments  3200 ,  3300  when forming the sphere puzzle  3400 .  
         [0214]     The sphere  3400  may also be formed by two of the hemispheres  3500  as shown in  FIGS. 35A  to  35 D, in which the various components are slidably movable relative to one another along their respective common surface.  
         [0215]      FIGS. 36A  to  36 D show various views of a hemisphere  3600  made up of four segments  3602  which are slidably movable relative to one another along their respective common surface. Two such hemispheres  3600  may be used for forming a sphere  3700  of FIGS.  37 A-D.  
         [0216]     The puzzle of the present invention may also use cylindrical rings.  FIGS. 38A  to  38 H show various views of an arcuate puzzle segment  3800 , and  FIGS. 39A-39D  and FIGS.  40 A-D show various views of two cylindrical rings  3900 ,  4000  conforming to the profile of the segment  3800 . Fifteen of the segments  3800  or two of the cylindrical rings  3900  and one cylindrical ring  4000  shown in FIGS.  40 A-D may be used for forming a puzzle part  4102  of a vessel  4100  shown in  FIGS. 41A  to  41 D. All components may be commonly shared with by adjacent cylindrical rings  3900 ,  4000 , and the edge fillers of the segments  3800  may also be shared by adjacent segments  3900 ,  4000 . A further cylindrical ring  4200  of FIGS.  42 A-D may comprise a component of the puzzle part  4102 , being engaged with the cylindrical ring  3900  for simultaneous rotational movement about their common longitudinal axis.  
         [0217]      FIGS. 43A  to  43 C show two arcuate puzzle segments  4300 ,  4302  conjoined with each other to form a sub-assembly  4304 . Eight such sub-assemblies  4304  may be combined to form a puzzle ring  4400  as shown in  FIG. 44 , in which the components are slidably movable relative to each other along their respective common surface. Three of the rings  4400  may be joined together in an orthogonal manner to form a puzzle part as shown in FIGS.  46 A-D, to be assembled on a core ball  4500  as shown in  FIGS. 45A  to  45 D. The rings  4400  may be moved along intersecting recesses  4502  of the ball  4500 . The recesses  4502  of the ball  4500  may be made according to the outline of the rings  4400 . The recesses  4502  may be smoothened, only leaving some slight interference between the recesses  4502  and the rings  4400 , so that the rings  4400  may seat in their proper positions. All components may be common parts throughout the three rings  4400  shown in FIGS.  46 A-D, and the edge fillers of any arcuate puzzle segment  4300 ,  4302  may also be shared by adjacent segments  4300 ,  4302  when forming the rings  4400 .  
         [0218]      FIGS. 47A  to  47 D show various views of a cylindrical ring  4700  with a number of interlocking puzzle units  4702 , which are slidably movable relative to one another along their respective common surface.  FIGS. 48A  to  48 D show various views of part  4802  of a cylindrical column. The part  4802  is formed of a number of interlocking puzzle units  4804 , which are slidably movable relative to one another along their respective common surface. Ten of the cylindrical rings  4700  or twenty of the cylindrical column parts  4802  may be combined to form the puzzle part  4902  of a cup  4900  shown in  FIGS. 49A  to  49 C. All the interlocking puzzle units  4702 ,  4804  may be commonly shared by adjacent cylindrical rings  4700  and cylindrical column parts  4802 .  
         [0219]     Puzzles made in accordance with the present invention may also use cylindrical rings and circular surfaces.  FIGS. 50A  to  50 D show various views of a ring  5000  with an internal circular cavity  5002  and six outer surfaces  5004  arranged in a regular hexagonal shape. Each of the outer surfaces  5004  has an inner semi-circular groove  5006 , and an outer semi-circular groove  5008 , arranged concentrically with each other.  FIGS. 51A  to  51 D show various views of a segment  5100 , being 1/6th of a circle and  FIGS. 52A  to  52 D show various views of a segment  5200 , being 1/12 of a circle. To form the puzzle part of a cup  5300  as shown in  FIGS. 53A  to  53 D, two of the rings  5000  engaged with each other, in which the open ends of the semi-circular grooves  5006 ,  5008  on each surface  5004  are aligned with one another to form two concentric circles. Six sectors  5100  are provided side by side in the inner circle formed by the semi-grooves  5006 , and twelve sectors  5200  are provided side by side in the outer circle formed by the semi-grooves  5008 . All sectors  5100 ,  5200  may be common parts shared by the surfaces  5004 .  FIGS. 54A  to  54 D show a puzzle  5400 , being a combination of two of the puzzle part of  FIGS. 53A  to  53 D.  
         [0220]     The cylindrical ring  5000  may be broken down into puzzle body components  5500  of  FIGS. 55A  to  55 D that may be moved along the recesses and protrusions of the intersection of two cylinders  5600  of  FIGS. 56A  to  56 D.  FIGS. 57A  to  57 D show a bare puzzle  5700 . All circular sectors may be common parts shared by adjacent circular surfaces. Also, the four puzzle body components of  FIGS. 55A  to  55 D  61  may be interchanged with other puzzle body components of this puzzle.  
         [0221]      FIGS. 93A  to  93 D show a cylindrical ring  9300  of sixteen tiles  9302 . Three of the rings  9300  may be joined together in an orthogonal manner to form the puzzle part of a ball  9400  as shown in  FIGS. 94A  to  94 D.  FIGS. 95A  to  95 D show inter-engagement of the rings  9300  and  FIGS. 96A  to  96 D show the inner ball  9600 . All the tiles  9302  may be commonly shared with other cylindrical rings. The embodiments shown in  FIGS. 94A  to  96 D may be developed to those shown in  FIGS. 43A  to  46 D.  
         [0222]     Further enhancements to the present invention may be also possible. In the above examples, not only have the puzzles been introduced, but the concept has been taught that the puzzles may be (or may further be) enhanced according to the above-mentioned methods or the combination of them. For example, the spherical sectors  4304  of  FIGS. 43A  to  43 D may be divided horizontally like the sector  3800  shown in  FIGS. 38A  to  38 D, if required, and many examples cited above may further be divided into hemispheres, as in the case of the sphere  3400  in  FIGS. 34A  to  34 D.  
         [0223]     The components for the puzzles of the present invention may be cut as follows. For the sake of illustration the present discussion will concentrate on spherical sectors since cutting a hemisphere, or cutting a component from cylindrical or circular surfaces is self-explanatory.  
         [0224]     It is possible to generate polyhedrons into a spherical shape.  FIGS. 58A-58D ,  59 A- 59 C,  60 A- 60 C,  61 A- 61 C and  62 A- 62 C show spheres generated from a cube, a dodecahedron, an icosahedrons, a tetrahedron and a 32-facet “soccer ball”, respectively. A sphere so generated should be concentric with the polyhedrons.  
         [0225]     A basic cutting rule is that all the arcuate puzzle segments in the present invention may be turned about its axis but must not be obstructed by the adjoining spherical sectors. Therefore, all the obstructions must be cleared. In fact, the obstructions may be the common areas between the adjoining segments. After the clearing action, fillers may be inserted to fill up the voids so created.  
         [0226]     The cutting tool may comprise, for purposes of illustration of the present invention, a face-milling cutter. The spindle of the cutter may be perpendicular to the work piece. Though a flat cutting face may be used for cutting majority of the arcuate puzzle segments so far discussed, it does not mean that only flat cutting faces may be used for cutting the segments. Flat cuttings planes may be chosen here for discussion because it is easier to indicate that the flat bottom of the segments may be turned on top of the flat surface formed by other segments.  
         [0227]     In fact, the cutting plane may be a flat plane, a cylinder or a cone surface of any arbitrary angle.  FIGS. 63A  to  63 D show an arcuate puzzle segment  6300  cut by a flat cutting plane.  FIGS. 64A  to  64 D show a sphere  6400  formed of six segments  6300 , with the obstructions cleared by a flat cutting plane.  
         [0228]      FIGS. 65A  to  65 D show a cone-shape cutting plane  6502  cutting a side of two arcuate puzzle segments  6504  at the same time.  FIGS. 66A  to  66 D show a sphere  6600  with the obstructions cleared by such a cutting plane. Components of the segments  3800  of  FIGS. 38A  to  38 D, and  4300  of  FIGS. 43A  to  43 C may be typical cone cutter examples—the vertex of the cone-shape cutting plane coincides with the center of the sphere.  FIGS. 67A  to  67 D show a reversed cone-shape cutting plane  6702  cutting two arcuate puzzle segments  6704  at the same time.  FIGS. 68A  to  68 D show a sphere  6800  with the obstructions cleared by such the cutting plane  6702 . The cutters for the fillers may be the inverse of the cutters described above, so that the filler side may be retained while the opposite side of the object at may be removed.  
         [0229]     Cylindrical cutting plane may be different from the above cutting planes. It may be like a drill or a core-cutter. It may be used for making way for the adjoining arcuate puzzle segments; therefore its diameter may be the same as that of the concerned adjoining segments.  FIGS. 69A-69B ,  70 A- 70 B,  71 A- 71 B,  72 A- 72 B, and  73 A- 73 B show how cylindrical cutting planes cut the components out. The cylindrical cutting planes may be drawn like a plate or a ring and placed at different heights aiming easy review. The cut components are also illustrated in  FIGS. 69C-69D ,  70 C- 70 D,  71 C- 71 D,  72 C- 72 D, and  73 C- 73 D. These components may be used for forming the segment  2500  shown in  FIGS. 25A  to  25 D. In particular, FIGS.  69 A-D show the center triangle being cut by three cylinders. The edge filler is cut by four cylinders, as shown in FIGS.  70 A-D, and by two hollow cylinders, as shown in FIGS.  71 A-D. The small filler may be cut by two hollow cylinders, as shown in FIGS.  72 A-D, and by two cylinders, as shown in FIGS.  73 A-D.  FIGS. 74A  to  74 D show a sphere  7400  assembled with these components.  
         [0230]     The arrangement of the cutting planes will now be further described. As mentioned previously, the polyhedrons have to be generated to spheres concentric to the original polyhedrons. The spindle of the cutter may be perpendicular to the flat facets of the polyhedron. Some examples are the arcuate puzzle segments  100  (FIGS.  1 A-D),  500  (FIGS.  5 A-D),  900  (FIGS.  9 A-D), and  3200  (FIGS.  32 A-D).  
         [0231]     The spindle of the cutter may also be in line with the axes of the vertexes of the sphere, e.g. an arcuate puzzle segment  7500  as shown in  FIGS. 75A  to  75 C, or a arcuate puzzle segment  7600  as shown in  FIGS. 76A  to  76 C. In fact, these two segments  7500 ,  7600  of the same icosahedrons but cut at different heights. Moreover, for better understanding of the invention, the vertex of the respective sphere is illustrated in  FIGS. 75D and 76D  respectively. Here may be some more examples—the triangle at the center of the segment  1400  in FIGS.  14 A-D may be the vertex of a tetrahedron; the center of the segment  2700  of FIGS.  27 A-D may be the vertex of a dodecahedron; and the center triangle of the segment  3300  of FIGS.  33 A-D may be the vertex of a cube.  
         [0232]     The spindle of the cylindrical cutter may also be perpendicular to the flat facets of the polyhedron or coincide with the axes of the vertexes of the sphere. The segment  2500  of FIGS.  25 A-D may be cut with a cylindrical cutter with a spindle perpendicular to the flat facet of the polyhedron.  
         [0233]     The cutting plane may also be any plane symmetrically bisecting the sphere. A combination of cutting planes for an object may also be possible. For example, the sphere  3400  of FIGS.  34 A-D may be built with the segment  3200  of FIGS.  32 A-D, or the segment  3300  of FIGS.  33 A-D, or the hemisphere  3500  of FIGS.  35 A-D.  
         [0234]     The structure of the present invention will be described in connection with the following methods. In a first method, the components are latched with each other, movable on top of the inner layer of the puzzle.  FIG. 77A  to  77 C show an exploded view of a few components in one embodiment of the present invention. It can be seen that three fillers  7704  latch underneath a central arcuate triangular component  7702 .  FIGS. 78A  to  78 D show a sphere  7800  built with the components  7702 ,  7704  of FIGS.  77 A-C, with one of the segments removed for showing an inner ball  7802 . FIGS.  79 A-C show an arcuate triangular component and FIGS.  80 A-C show a filler  8000 , which may be combined to form the sphere  1600  as shown in FIGS.  16 A-D. Undercuts may be added to the required position of the components whenever necessary, to be further discussed below.  
         [0235]     To facilitate the assembly operation, the lastly assembled filler may be split into two, upper and lower halves which may later be snapped back together or joined back with screw, glue, solvent, sonic welding, heat-staking and whatever possible means. Similarly, other components with undercut portions may be similarly formed, as illustrated hereinafter, and they may be broken down into sub-components and assembled back afterwards.  
         [0236]     Undercuts may be added to the required position of the puzzle components whenever necessary (to be further discussed below) to prevent the components from going sideway. However it is also possible to instead fix the center component on the inner ball.  
         [0237]     Returning to undercuts,  FIGS. 81A  to  81 D show a puzzle component  4702  of the ring  4700  of  FIGS. 47A  to  47 D or a component  4804  of the part  4802  of  FIGS. 48A  to  48 D. It can be seen that the puzzle component  4702  has on a side a trapezoidal extension/latch  4712 , and on an opposite end a correspondingly shaped and sized trapezoidal recess  4714 . By way of such an arrangement, an extension  4712  of a first puzzle component  4702  may be received within a recess  4714  of a second puzzle component  4702 , as in the case of a dovetail joint, whereby the two puzzle components  4702  are inter-engaged with each other, such that while one of the components  4702  may be slidably movable relative to the other component  4702  parallel to the bi-directional axis L-L shown in  FIG. 81D , they cannot be otherwise movable from each other.  
         [0238]     Furthermore, a third side of the component  4702  is provided with an L-shaped extension/latch  4716 , and a correspondingly shaped and sized L-shaped recess  4718  is provided on a side opposite to the third side. By way of such an arrangement, an extension  4716  of a first puzzle component  4702  may be received within a recess  4718  of a second puzzle component  4702 , whereby the two puzzle components  4702  are inter-engaged with each other, such that while one of the components  4702  may be slidably movable relative to the other component  4702  parallel to the curved bi-directional axis M-M shown in  FIG. 81C , they cannot be otherwise movable from each other.  
         [0239]     Pegs may be employed to replace some of the latches. Regarding the same sphere  1600  shown in  FIG. 16 , there may be two additional components—an elastic spring disc  8200  as illustrated in  FIGS. 82A  to  82 D, and a peg  8300  as shown in  FIGS. 83A  to  83 D. The peg  8300  has a wider outer disc  8302 , a narrower inner disc  8304  and a post  8306 .  FIG. 84  shows an inner ball assembled with a number of the spring discs  8200  and pegs  8300 , in which, in order to reveal all the components, the outer disc  8302  of the pegs  8300  has been removed.  FIG. 85  shows the inner ball as assembled with a number of the spring discs  8200  and the actual pegs  8300 . The spring disc  8200  may be the foot of the triangle. After the triangles  8602  are assembled on the spring discs  8200 , the sub-assembly should look like  FIG. 86 . For purposes of illustration, the fillers are not shown.  
         [0240]     The structure may be such that all twelve pegs  8300  are fixed on the inner ball while the spring discs  8200  may revolve round the pegs  8300 . The spring disc  8200  may be so designed that it may contact the inner discs  8304  of, and hold position among, the three pegs  8300  around it. However, during revolution about the axis of the peg  8300 , the spring discs  8200  may shrink while passing through the pegs  8300 . Anyway, a weak spring force may be good enough. The main idea is that the outer disc  8302  of the peg  8300  should trap the inner part of the puzzle member, i.e. the spring disc  8200  of the triangle  8602 , from dropping out.  
         [0241]     In another example,  FIGS. 97A  to  97 D show a square peg  9700 , and  FIGS. 98A  to  98 D show an arcuate puzzle segment  9800 , being in the form of 1/8th of a sphere.  FIG. 99  shows six pegs  9700  and eight segments  9800  assembled on the inner ball, with the top layers of the pegs  9700  and that of the segments  9800  hidden to reveal the assembly.  FIG. 100  shows the actual pegs  9700  in the assembly.  FIGS. 101A and 101B  show the complete sphere. The hemisphere made with four segments  9800  may revolve about the axis of the peg  9700  of FIGS.  97 A-D.  
         [0242]     As a further example,  FIGS. 102A  to  102 D show a triangular peg  10200 , and  FIGS. 103A  to  103 C show an arcuate puzzle segment shell  10300 , being in the form of 1/4th of a hemisphere. It can be seen that the segment shell  10300  has three in-turned undercut portions  10302 , each at an angle of the segment shell  10300 .  FIG. 104  shows a sphere  10400  assembled with the peg  10200  of FIGS.  102 A-D, and the segments  10300  of FIGS.  103 A-C, but with the top layer removed for showing the assembly.  FIGS. 105A and 105B  show that the inner ball may be assembled to the sphere of  FIG. 104 , with four of the segments  10300  hidden. The appearance of the fully assembled sphere is the same as the sphere  3700  of FIGS.  37 A-D. A hemisphere made with four of the segments  10300  of FIGS.  103 A-C may be turned along the four pegs  10200  on the same hemisphere. For the above two examples, one of the segments  10300  may need to be fixed on the inner ball or the peg  10200  underneath it in order to keep all the segments  10300  and pegs  10200  on the proper tracks.  
         [0243]     In a third method, the inner ball may be replaced by a skeleton, which may provide each arcuate puzzle segment a pole for assembly. Then the components of that segment may be rotated about the axle of the corresponding pole.  FIGS. 87A  to  87 D show such a skeleton  8700 .  FIGS. 88A  to  88 D show an exploded view of the skeleton  8700  with components of the segment  900  of FIGS.  9 A- 9 G Since all components of the sector  900  may be latched with each other, the skeleton  8700  only needs to be fixed with the triangle at the center of the spherical sector  900 . FIGS.  10 A-C show the fully assembled sphere  1000 .  
         [0244]     In a fourth method, the components may be trapped in an undercut groove. For example, the components of FIGS.  51 A-D and  52 A-D may be trapped inside the undercut groove  5006 ,  5008  of FIGS.  50 A-D or that of FIGS.  55 A-D. In fact, as long as the components of FIGS.  51 A-D and  52 A-D do not drop out from the fences of the grooves of FIGS.  50 A-D or  55 A-D, they may be of other shapes, say, circular or spherical shapes. Moreover, the mating circular surfaces of the body (i.e., that shown in FIGS.  50 A-D or  55 A-D) and the components (i.e., that shown in FIGS.  51 A-D and  52 A-D) may be flat or of cone shape or spherical shape.  
         [0245]     A fifth method may be provided, which may be a combination of the above four methods. For example, with regard to the sphere  3400  of FIGS.  34 A-D, the first method may be adopted for most components and the second method for the components at the rim of the hemispheres. There may be still many other possible combinations within the spirit and scope of the present invention.  
         [0246]     The surface of the puzzle may be protruded to any shape as long as no portion of any components goes beyond any of the cutting planes of the components. For example the shape of the puzzles may be made back to the shape of the original polyhedrons as long as no profile of any component interferes with any of the cutting planes. In addition, the puzzles generated from the present invention may also take the form of shapes of popular characters (e.g., cartoon characters or the like).  
         [0247]     As another example,  FIGS. 89A  to  89 D and  90 A to  90 D show two different halves of the shape of the 3-dimensional puzzle  9100  of  FIGS. 91A  to  91 D, which may be basically a sphere, but modified to an odd-shaped object formed with three cylinders intersected together. Since components of the modified shape do not cut any of the cutting planes, therefore all components, like the sphere  3700  shown in  FIGS. 37A  to  37 D, may be shared with the adjacent halves or hemispheres.  FIGS. 92A  to  92 C show another example demonstrating that although the sphere  3700  of FIGS.  37 A-D has been modified to a long rod, halves of such rod may still be turned about the three orthogonal planes. In particular,  FIGS. 92A  to  92 C show the same puzzle with different halves turned by 45°.  
         [0248]      FIGS. 106A  to  106 C show, respectively, an arcuate puzzle segment, being in the form of 1/6th of a sphere shell  10602 , a rail  10604  for holding adjacent segments  10602  together, and a hexagonal peg  10606 , for forming a sphere  10702  as shown in  FIG. 107A . As shown in  FIG. 106A , the segment  10602  has an outer layer  10602   a  and a narrower inner layer  10602   b . The same sphere  10702  is shown in  FIG. 107B  with a top layers  10602   a  of the segments  10602  removed.  FIG. 108A  shows an inner ball  10802  of the sphere  10702 , with the rails  10604  and pegs  10606  removed, whereas in  FIG. 108A , only the “naked” rails and pegs are replaced, in the sense that the respective outer layers of the rails and pegs are removed for revealing the interior structure. The two pegs  10606  are fixed diametrically on the inner ball  10802 , whereas the rails  10604  are movable relative to the inner ball  10802 . A hemisphere made with three shells  10602  may thus revolve together with two rails  10604  engaged underneath.  
         [0249]     As a further example,  FIG. 109A  shows a peg  10902  with a wider outer layer  10902   a  and a narrower inner layer  10902   b  fixedly secured with each other.  FIG. 109B  shows an arcuate puzzle segment shell  10904 , being in the form of 1/6th of a sphere, which is slidable over and relative to the peg  10902 . As shown in  FIG. 109B , the segment shell  10904  has an outer layer  10904   a  provided with a hook portion  10904   b  at each longitudinal end.  
         [0250]      FIG. 110A  shows a sphere  11000  formed of six segment shells  10904  and six pegs  10902 , and  FIG. 110B  shows the same sphere  11000  but with the outer layer  10904   a  of the segment shells  10904  removed, thus showing only the hook portion  10904   b .  FIG. 111A  shows the same sphere  11000 , but with three segment shells  10904  removed. As to  FIG. 111B , such shows the inner ball  11100  with only the inner layers  10902   b  of the peg  10902  and the hook portions  10904   b  of the segment shells  10904 . It can be seen that, by way of this arrangement, and with the pegs  10902  fixed on the inner ball  11100 , and with one of the segment shells  10904  fixedly engaged with the inner ball  11100  or with the peg  10902  underneath it, the segments shells  10904  may be slidably movable relative to one another along their common surfaces.  
         [0251]      FIG. 112A  to  112 F show various views of an arcuate puzzle segment shell  11200 , being in the form of 1/4th of a hemisphere, with three tracks  11202  running on its inner surface and alongside its three sides.  FIG. 113  shows a peg  11300 , having a generally square base  11302  provided with four quarter-circle extensions  11304  each adjacent a corner of the base  11302 . The extensions  11304  are sized and configured to be received within the tracks  11300  for relative sliding movement. By way of such an arrangement, and as shown in  FIG. 114 , it is possible to secure all eight segment shells  11200  on an inner ball  11400  by three pegs  11300  fixedly on the inner ball  11400 , so that the segment shells  11200  may be moved relative to one another along their common surfaces. Of course, for better engagement between the inner ball  11400  and the segment shells  11200 , more pegs  11300  may be provided.  
         [0252]     As an alternative, rows of movable pegs  11300   a  may be provided, as shown in  FIG. 115 , between the fixed pegs  11300 . As a further alternative, instead of having rows of movable pegs  11300   a , a movable rail  11600  (as shown in  FIG. 116B ) may be positioned between two fixed pegs  11300  (as shown in  FIG. 116A ) for bridging the fixed pegs  11300 . All the additional pegs  11300   a  and rails  11600  are not fixed on the inner ball  11400 .  
         [0253]     As a still further alternative,  FIG. 117A  shows an arrangement similar to that shown in  FIG. 115 , but with fixed pegs  11700  (as shown in  FIG. 117B ) having square extensions instead of quadrant extensions. Similarly,  FIG. 118  shows the use of rails  11800  for bridging the fixed pegs  11700 .  
         [0254]      FIG. 119A  shows a further arcuate puzzle segment shell  11900 , being in the form of 1/4th of a hemisphere, and  FIG. 119B  shows a peg  11902 . The segment shell  11900  has three tracks  11904  running along and parallel to the three sides of the segment shell  11900 . The peg  11902  has a circular base  11906  and four quarter-circle extensions  11908 . The peg  11902  and its extensions  11908  are sized and configured such that two parallel ridges  11910  lying side by side, one for each segment  11900 , may be received within the spaces between the extensions  11908 , and the extension  11908  may be received within the track  11904  for relative sliding movement.  
         [0255]     Thus, as shown in  FIG. 120 , a puzzle sphere  12000  may be formed of an inner core globe  12002  fixed with a number of pegs  11902 , over which are engaged with eight of the segment shells  11900 . One of the segment shells  11900  may be fixed with the peg  11902  underneath it or with the inner ball  12002 . Similar to the example discussed above, rows of pegs  11902   a  may be provided between the pegs  11902  (as shown in  FIG. 121 ); or rails  12200  (as shown in  FIG. 122B ) may be provided between the pegs  11902  (as shown in  FIG. 122A ).  
         [0256]      FIGS. 123A  to  123 E show various views of an arcuate puzzle segment shell  12300 , being in the shape of 1/4th of a hemisphere;  FIG. 124B  shows a peg  12400 ; and  FIG. 124C  shows a rail  12402 . It can be seen that on an inner surface of the segment shell  12300  are provided with three undercuts  12302 , each running parallel to and alongside a side of the segment shell  12300 . As to the peg  12400 , there is a central square protrusion  12404  surrounded by four recesses  12406 , each forming a track adapted to receive an undercut  12302  for relative sliding movement. As to the elongate rail  12402 , such includes two parallel tracks  12408 , each being of the same width as, and for alignment with, the recesses  12406  of the peg  12400 . With the arrangement as shown in  FIG. 124A , an inner ball  12410  is fixed with a number of pegs  12400  with the recesses facing the inner ball  12410 . A number of rails  12402  are positioned between the pegs  12400  for bridging the pegs  12400 . The segment shells  12300  may thus be engaged onto the inner ball  12410  by having the undercuts  12302  received within the recess of the pegs  12400  and the tracks  12408  for relative sliding movement.  
         [0257]      FIGS. 125A  to  125 D show various views of an arcuate puzzle segment shell  12500 , being in the shape of 1/4th of a hemisphere;  FIGS. 126B and 126D  show a rear perspective view and a front perspective view of a peg  12600 ; and  FIG. 126C  shows a rail  12602 . As shown in  FIG. 126A , an inner ball  12604  is fixed with a number of pegs  12600  with their respective intersecting recesses  12606  facing outwardly. The rails are positioned between and bridging the pegs  12600 , with a central track  12608 , also facing outwardly, and in alignment with the recesses  12606  of the pegs  12600 . A number of continuous intersecting tracks are thus provided on the inner ball  12604 . As to the segment shell  12500 , such is provided with three ridges  12502 , each running parallel to and along a respective side of the shell  12500 . By way of such an arrangement, the shell  12500  may be engaged with the pegs  12600  and the rails  12602  for relative sliding movement.  
         [0258]     Although the undercuts have thus far been shown as in a generally “L” shape, it is possible to have in the shape of a straight slope (as in the case of the arrangement shown in  FIGS. 127A  to  127 D), a curved slope or an irregular slope.  
         [0259]     In the examples discussed above, the arcuate puzzle segment shells, in the assembled puzzle, cover the pegs and the rails. It is, however, possible to add a raised rib on the rail (as shown in  FIG. 128A ), and a post on the peg (as shown in  FIGS. 128B  to  128 D), so as to reveal the positions of the pegs and rails in the assembled puzzle sphere, as shown in  FIGS. 129A and 129B . With sufficient rails and pegs, a puzzle globe (e.g. bearing a world map thereon) may be provided, as shown in  FIGS. 130 and 131 A to  131 C, with the ribs being the longitudes and the equator. Such raised ribs and posts may be applied to other puzzles.  
         [0260]     Instead of providing ribs or posts which extend beyond the outer surface of the segment shells in the assembled puzzle globe, it is possible to widen the post or ribs to form the puzzle globe  13200  as shown in  FIGS. 132A  to  132 D. In this puzzle globe  13200 , the pole positions  13202  are formed of two semicircles only. Similarly, such widened posts and ribs may be applied to other puzzles.  
         [0261]     As a general summary, and as shown in the above examples, the pegs may be of a variety of shapes and configurations; the space between the pegs may be filled with pegs or rails; the undercuts may be provided by flanges extending inwardly or outwardly from the pegs; the undercuts may also be provided by flanges extending upwardly or downwardly from the segment shells; the undercuts may be of a generally “L” shape, a straight slope, a curved slope, or an irregular slope; a post may be provided on the peg; and a raised rib may be provided on the rail.  
         [0262]     As a further embodiment of the present invention,  FIG. 133A  shows a fluted inner ball  13300  and an arcuate puzzle segment shell  13302 , being in the form of a 1/6th of a sphere. It can be seen from  FIG. 133B  that a circular extension  13304  is provided on an inner surface of the shell  13303 .  FIG. 134A  shows a puzzle sphere  13400  formed of the inner ball  13300  and six segment shells  13302 . The same assembled puzzle sphere  13400  is shown in  FIG. 134B , but with the outer shells removed, thus showing only the circular extensions  13304  only. It can be seen that the circular extensions  13304  are received within undercuts of the fluted inner ball  13300  for retaining the segments  13302  on the inner ball  13300  for relative movement.  
         [0263]     As an alternative, the undercuts may be provided on the inner surface of the arcuate puzzle segment shell, and the pegs be provided on the surface of the inner ball, as shown in  FIGS. 135A, 135B ,  136 A and  136 B.  
         [0264]     FIGS.  137 A-D,  138 A-D,  139 A-D and  140 A-D show various vessels/containers, each bearing a puzzle part. It is of course possible to form caps bearing a puzzle part. On the other hand, FIGS.  141 A-D,  142 A-D,  143 A-D and  144 A-D are modified versions of puzzles generated from previously discussed puzzles, but with different cutting planes.  
         [0265]     It is possible to provide further layer(s) onto the puzzles so far discussed above. For example,  FIGS. 145A and 145B  show two exploded views of a puzzle. The core puzzle  14500  is the one as shown in FIGS.  142 A-F. When the outer components are fixed (either releasably or not) onto the core puzzle  14500 , such will form the puzzle as shown in  FIGS. 143A  to  143 D.  
         [0266]     The puzzle shown in FIGS.  146 A-C is modified from the one shown in FIGS.  24 A-C.  FIG. 147  is an exploded view showing the addition of further components onto the puzzle in FIGS.  146 A-C. With such an arrangement, it is possible to shape the further components such that the resultant puzzle resembles any desired shape or configuration, e.g. the head of an animal. In particular, FIGS.  145 A-B and  147  thus show that puzzles according to the present invention may be snapped on with another outer layer which may be rather thick, so as to allow the resultant puzzle to be formed into various contours or animal shapes.  
         [0267]     While various preferred embodiments of the present invention have been disclosed and described in detail herein, it will be apparent to those skilled in the art that various changes in form and detail may be made thereto without departing from the spirit and scope thereof.  
         [0268]     For example, the drawings in this presentation are conceptual drawings only. In actual design, clearance between components may be provided and various parts would be slightly rounded to prevent sharp corners, sharp edges, and the like. In addition, one can apply any combination of the above-discussed shapes into in an actual design. Moreover, if the puzzle components are too smooth for manipulation, the surface may be textured wherever necessary.