Patent Publication Number: US-2005136794-A1

Title: Interconvertible soft articles

Description:
This is a continuation-in-part application of application Ser. No. 10/151,519, filed May 20, 2002, entitled Interconvertible Soft Articles, by G. Blonder, which application is hereby incorporated herein by reference in its entirety. 
    
    
     1. FIELD OF THE INVENTION  
      The invention is directed to interconvertible articles constructed of soft, resilient material for educational use and amusement.  
     2. BACKGROUND OF THE INVENTION  
      Interconvertible toys, which interconvert from one geometry to another, promote interest in geometry and provide visual stimulation to children and adults alike. Interconvertible toys that take on a substantially different geometry upon an exterior to interior interconversion are particularly fascinating. When constructed from soft material, interconvertible toys are advantageous because they are safe for small children and easily manipulated. Many prior-art soft, interconvertible toys, however, are limited in complexity of movement and visual effect. With many prior art soft, interconvertible toys, after the child intentionally converts the toy from one geometry to another, the lack of ruggedness or robustness results in the toy flipping geometry under normal playing conditions.  
      U.S. Pat. No. 5,433,647 (issued Jul. 18 1995) by B. Ciquet (“Ciquet”) discloses soft, interconvertible articles constructed by dissecting a single piece of elastic foam material. Because the article is constructed from a single piece of foam, the variety of visual and mechanical effects is limited. None of Ciquet&#39;s articles are both stable and robust. While Ciquet&#39;s articles may be interconverted from one geometry to another, disadvantageously, upon such interconversion, stress is concentrated at the interconversion points. Such stress can cause deterioration and eventual failure of the article. Moreover, in many of Ciquet&#39;s designs, upon interconversion from a first to a second geometry, there is a build up of internal compressive forces such that the second geometry is not in a zero energy state. Such internal forces may cause the article to spontaneously snap out of the unstable second geometry back into the first geometry. In other examples, Ciquet&#39;s articles are unstable, floppy and limp therefore lacking a visually stimulating effect upon interconversion.  
      U.S. Pat. No. 5,115,528 (issued May 26, 1992) by S. Lamle (“Lamle”) discloses the typical reversible bag- or pillow-type toy where the basic geometry is retained after transformation, but the geometry inside the bag after “stuffing” is greatly distorted. And the geometry outside the bag is not fixed, but changes depending on how the toy was last handled. Such an article lacks the same stimulating visual and geometrically puzzling effects obtained upon a true interconversion.  
      U.S. Pat. No. 5,310,378 (issued May 10, 1994) by S. Shannon (“Shannon”) discloses toys transformable between open and closed conformations. These toys, however, can only nest appendages into matching recesses and, therefore, lack a substantial visual effect. They are not interconverted or inverted.  
      In view of the above, there is a need for stable and robust, soft interconvertible articles that provides a significant visual effect upon interconversion. The discussion of references in this Background Section 2 is provided for background purposes only and no assertion, statement, or admission is made regarding the references&#39; prior art status with respect to the invention.  
     3. SUMMARY OF THE INVENTION  
      The invention relates to stable, robust and soft interconvertible articles that take on a substantially different geometries, which are also stable and robust, upon interconversion, to provide a significant, surprising visual effect. Quite startling effects accompany this interconversion, including exchange of colors and textures and up to tripling the exterior surface area. The articles of the invention are useful as educational aids and for amusement, magic tricks, etc. and, thus, provide learning and fun for both children and adults.  
      In one embodiment, the invention provides an article comprising a first stable and robust geometry in a zero energy state and a plurality of soft, resilient members interconnected by hinge-type connections, wherein the article adopts a second stable and robust geometry in a zero energy state after application of an applied force approximating or approaching an interconversion force.  
      In a preferred embodiment, when the applied force approaches or approximates the interconversion force, a quantum of stored energy within the article propels the article into the second geometry. 
    
    
     4. BRIEF DESCRIPTION OF THE FIGURES  
      These and other features, aspects, and advantages of the present invention will become better understood with regard to the following description, appended claims, and accompanying drawings where:  
       FIG. 1  shows three views of a flat plate interconverting toy that is unstable, and thus not representative of this application.  
       FIG. 2  are four views of a block of foam connected by hinges, to illustrate the difference between stability and robustness.  
       FIG. 3  is a plot graphically indicating the response of the block in  FIG. 9  to external forces, such as those encountered in play.  
       FIG. 4  shows two views of a flat plate interconverting toy that is unstable, and thus not representative of this application. The toy is unstable because of the limited number of hinges and the compressive forces in one geometry.  
       FIG. 5  shows a toy doll in three different positions after play.  
       FIG. 6  is a plot graphically indicating the response of the doll in  FIG. 11  to external forces, such as those encountered in play.  
       FIG. 7  shows three different assemblies to illustrate the effect of hinge placement on the robustness of the linked members.  
       FIG. 8A  is a perspective view of an article of the invention having a cube geometry that can be interconverted to an article of the invention having a stellated-cube geometry;  
       FIG. 8B  is a perspective view of the article of the invention shown in  FIG. 8A  illustrating the initiation of interconversion into an article of the invention having a stellated-cube geometry;  
       FIG. 8C  is a perspective view of an article of the invention having a stellated-cube geometry that can be interconverted to an article of the invention having a cube geometry;  
       FIG. 8D  is a graphical representation of interconversion of cube  1   a  to stellated cube  1   b , wherein the x-axis is time, the left y-axis is applied force, and the right y-axis is the stored potential energy;  
       FIG. 9A  is an exploded view of the article of the invention shown in  FIG. 8A ;  
       FIG. 9B  is an exploded view of the article of the invention shown in  FIG. 8C ;  
       FIG. 10A  is a perspective view of an article of the invention having a building-shaped geometry that can be interconverted to an article of the invention having a car-shaped geometry;  
       FIG. 10B  is a perspective view of the article of the invention shown in  FIG. 3A  illustrating the initiation of interconversion into an article of the invention having a car-shaped geometry;  
       FIG. 10C  is a perspective view of an article of the invention having a car-shaped geometry that can be interconverted to an article of the invention having a building-shaped geometry;  
       FIG. 11  is an exploded view of the article of the invention shown in  FIG. 10C ;  
       FIG. 12A  is a perspective view of an article of the invention having a disk-shaped geometry that can be interconverted to an article of the invention having a sun-shaped geometry;  
       FIG. 12B  is a perspective view of the article of the invention shown in  FIG. 5A  illustrating the initiation of interconversion into an article of the invention having a sun-shaped geometry;  
       FIG. 12C  is a perspective view of an article of the invention having a sun-shaped geometry that can be interconverted to an article of the invention having a disk-shaped geometry;  
       FIG. 13  is an exploded view of the article of the invention shown in  FIG. 12A ;  
       FIG. 14A  is a perspective view of an article of the invention having a icosahedron geometry that can be interconverted to an article of the invention having a stellated-icosahedron geometry;  
       FIG. 14B  is a perspective view of the article of the invention shown in  FIG. 14A  illustrating the initiation of interconversion into an article of the invention having a stellated-icosahedron geometry;  
       FIG. 14C  is a perspective view of an article of the invention having a stellated-icosahedron geometry that can be interconverted to an article of the invention having a icosahedron geometry; and  
       FIG. 15  is an exploded view of the article of the invention shown in  FIG. 14C .  
    
    
     5. DETAILED DESCRIPTION OF THE INVENTION  
     5.1 Definitions  
     5.1.1 Distortion Force  
      As used herein, the term distortion force means the minimum quantum of force required to distort an object from its original shape and geometry into a different shape and geometry. The value of a distortion force depends on the rigidness and resiliency of the subject article. For example, the distortion force with respect to a sock is much less than the distortion force of a foam-rubber football, and very much less than the distortion force of a glass. It should be noted that when a distortion force is applied to a glass, the glass breaks.  
     5.1.2 Stable  
      As used herein, the term “stable” with respect to an article means that the article reverts back to its original definite shape after a distortion force is released. In general, articles that are floppy, limp, sagging, or droopy are not stable. For example, a sock is unstable because if distorted at all, for example picked up, it is limp and floppy and when placed back down, it does not revert back to its original shape or geometry. Conversely, a foam rubber cube ottoman is distorted into an oblate sphere when sat upon, but returns to the original cubic shape when the sitter rises. The foam is stable.  
     5.1.3 Robust  
      As used herein, the term “robust” with respect to a robust geometry, different from the above definition of “stable”, means that the geometry can be subjected to forces larger than mere distortion forces, such as large compressive forces and spontaneously return to the geometry exhibited before the large force was applied. For example, a rubber kick-ball distorts into a disk when thrown against a wall, but returns to a sphere immediately afterward, even when thrown with extreme force. Thus, a kick ball is “robust”. An article may be stable but not robust, for example, it may be stable enough to be gently examined and rotated by hand, but not stable enough to be thrown against a wall and return to its original geometry.  
     5.1.4 Robustness versus Stability  
       FIG. 1  assists in understanding the difference in meaning between “stable” and “robust”. As shown in  FIG. 1 , geometry  142  is held together by four hinges. These four hinges will not prevent the plate-shaped body from folding into a diamond geometry  143  under the application of a distortion force. For planar structures, the well known Euler Law states a series of linkages are robustly stable if: 
   E =2V−3.  
 E is the number of edges, and V is the number of vertices (hinges) in a view perpendicular to the motion. In  142 , there are four edges and four hinges, so: 
 4≠2*4−3  
 and the Euler Law is not satisfied. In the article of  FIG. 1 , robust stability under the Euler Law requires a diagonal brace, bringing E up to five. 
 
      To further explain the difference between stability and robustness, consider a rectangular article on a table as shown in  FIG. 2 . This article consists of two foam blocks,  911  and  912 , connected by a flexible hinge  913 . In first position  91 , the geometry is stable, but not robust to a force F 1 . That is, a small F 1  (i.e., a distortion force) will tilt the top block  911  to semi-open position  92 , but when F 1  is released, the brick returns to position  91 . Accordingly, the object is stable with respect to force F 1 . A larger force, however, will cause the brick to tip over and lay flat, as in  93 , unable to return to the original geometry  91  without the application of additional force. Had it resisted the larger distorting force F 1 , and returned to original geometry  91  after application of F 1 , the brick would be “robust”.  
      A graphical description of the sequence described above is helpful. The graph in  FIG. 3  shows time along the horizontal axis. Force is plotted on the positive vertical axis, while the shape or position of the article is illustrated on the negative vertical axis. As can be seen in this graph, a series of forces are applied and withdrawn on the brick. At time=3 and time=7, the brick tilts but returns to position  91 . However, at time=10, the force is large enough to tilt the brick over into position  93 .  
      Of course, bricks  911  and  912  could be made robust by adding an additional hinge  914  as seen in  94  of  FIG. 2 . While stable and robust, the arrangement shown in  94  cannot interconvert because  911  and  912  can not fit within the interior. Still, in general, more hinges increase the likelihood of a robust structure.  
      Finally, consider the soft, interconvertable doll depicted in  FIG. 5  to illustrate an unstable article. Very small forces can rearrange the members&#39; (e.g., the arms, legs, head) positions, and thereby change the geometries between  111 ,  112  and  113 . As seen in the  FIG. 6  graph, every time a distortion force is applied to the doll, it adopts a new geometry. Even when forces are not applied, as between time=5 and time=6, the fabric might sag and change shape under the influence of gravity or stored elastic forces. In this case we say the toy&#39;s geometry is “unstable”.  
     5.1.5 Zero Energy State  
      As used herein, the phrase “zero energy state” with respect to an article of the invention means that there are little or no internal mechanical stresses (i.e., potential energy) within the article. For example, there is no internal mechanical stress created by rotatable members in an article in a zero energy state. To illustrate this concept,  FIG. 4  depicts a four-member, flat plate, wherein element  1622  is a square. As such, when interconverted into geometry  162 , element  1622  is distorted and exerts a compressive force on adjacent elements  1624  and  1625 . This internal compressive force may spontaneously convert the article back into position  162 , even in the absence of an external event such as dropping the article on the floor. As such, the geometry depicted in  162  of  FIG. 4  is not in a zero energy state.  
     5.1.6 Interconversion Force  
      As used herein, the phrase “interconversion force” with respect to an article of the invention means the mechanical force required to be applied to an article of the invention to interconvert it from a first stable and robust geometry to a second stable and robust geometry.  
       FIG. 8D  is a graphical representation of interconversion of cube  1   a  to stellated cube  1   b , wherein the x-axis is time, the left y-axis is applied force, and the right y-axis is the potential energy stored in the toy. Note that when the applied force is zero, the stored energy is zero (e.g., at time=0). As the force increases from zero to the distortion force, more and more potential energy is stored in the mechanical compression and twisting of the compressible members and hinges. Finally, when the force reached the “interconversion” force around time=2, the stored energy is near maximal. After removing the force, the stored energy propesls the interconversion into the second stable and robust geometry, a process which is completed at time=3. Note the stored energy is zero upon completing interconversion. In other words, when the applied force approaches or approximates the interconversion force, a quantum of stored energy within the article propels the article into the second geometry.  
     5.1.7 Hinge-Type Connection  
      As used herein, the phrase “hinge-type connection” means any type of flexible connection interconnecting members at their edges. The only requirement is that the connection allow for hinge-type movement of the member, and that the hinge itself can be bent during the transition, but recovers elastically from that distortion. Examples of hinge-type connections suitable for use in the invention include, but are not limited to, stitches, staples, or pins joining fabric strips, VELCRO, zippers, rings, or fabric encompassing two or more members, the fabric having a dividing seam between the members. Preferably, the hinges are formed via a soft fabric layer encompassing two or more members, the fabric layer having stitched dividing seams between the members. In other words, the soft members are interrelated through a fabric covering and the hinge-type connections comprise intersection of the fabric covering. Any type of fabric may be used, and will be chosen based on desired qualities of the interconvertible articles of the invention.  
     5.1.8 Member  
      As used herein, the term “member” means any object, of any shape, and of any material, wherein the member is part of an interconvertible article of the invention. A “rotatable member” means a member designed to be turned, rotated, or twisted via a hinge-type connection concomitantly with one or more other rotatable members thereby effecting interconversion of an article of the invention.  
     5.1.9 Soft, Resilient Member  
      As used herein, the phrase “soft, resilient member” means any object of any shape made from any soft, resilient material, wherein the member is part of an interconvertible article of the invention. “Soft” means that the member is readily deformable on touch; for reference purposes, examples of soft objects are pillows, air-filled balloons, foam rubber, etc. “Resilient” means that the member assumes its original shape once the stress that induced distortion is removed. Preferably, a resilient member is compressible to the extent of from about 50% to about 90% of its volume and, upon release of the compressive force, assumes its original shape in less than about three seconds. Suitable soft, resilient materials for use in the invention include, but are not limited to, foamed plastics such as latex or urethane open-cell foams, air-filled elastic latex balloons, or fabric bags filled with spun stuffing, made for example from cotton, goose down, or nylon. Preferably, the soft, resilient members are covered with colorful or otherwise appealing fabric. These fabrics can be slightly elastic (by co-weaving with rubber), metallized, made from “fake fur”, or tough rip-stop nylon normally used in backpacks.  
     5.1.10 Interior Surface Area  
      The phrase “interior surface area”, with respect to a soft, resilient members in an article of the invention in a particular robust geometry, means that portion of the member&#39;s surface area that is not visible because it is enclosed or shielded from sight within the article. For example, with respect to  FIG. 8B  (discussed in more detail below), the interior surface area of member  2   a  of article  1  in conformation  1   a , consists of the surface area of the four triangular faces  8 . The exterior surface of an article means the visible surface area not enclosed within the article.  
     5.1.11 Interconvertible Interior Surface Area  
      As used herein, the phrase “interconvertible interior surface area”, with respect to an article of the invention, means that portion of the member-defined interior surface area that is exchanged to the article&#39;s exterior surface upon interconversion. See for example  FIG. 9B , discussed in more detail below, where the sum total surface area of bases  10  define the interconvertible interior surface area if article  1  in geometry  1   b.    
     5.1.12 Interconversion or Interconverting  
      As used herein, the term “interconversion” or “interconverting” with respect to a rotatable member means moving or rotating the member such that there results an exchange of a portion of the member&#39;s interior surface area to the exterior surface.  
     5.1.13 Interconversion or Interconverting  
      As used herein, the term “interconversion” or “interconverting” with respect to an article of the invention means turning, rotating, or twisting one or more of the rotatable members such that there results an exchange of the article&#39;s interconvertible interior surface area to the article&#39;s exterior surface. See for example,  FIGS. 8A-8C , discussed in more detail below, wherein article  1  in geometry  1   a  is interconverted to geometry  1   b  by interconverting rotatable members  2 . Preferably, interconversion is accomplished by pushing one or more rotatable members through a gap between a small number of members, such gap referred to herein as an “interconversion opening” (see  7  in  FIG. 8 ). Preferably, upon interconversion, an article of the invention converts from a first robust geometry to a second robust geometry. Additionally, upon interconversion the members maintain their original shape in the second robust geometry that they had in the first robust geometry, even after experiencing active play. Thus, while deformation of the members occurs during interconversion or play, the individual members, due to their resiliency and the geometric arrangement of the hinges, assume their original shape in the second robust geometry, as well as their geometric relationship to all other members.  
      In one embodiment, the invention provides an article comprising a first stable and robust geometry in a zero energy state and a plurality of soft, resilient members interconnected by hinge-type connections, wherein the article adopts a second stable and robust geometry in a zero energy state after application of an applied force approximating or approaching an interconversion force.  
      In a preferred embodiment, when the applied force approaches or approximates the interconversion force, a quantum of stored energy within the article propels the article into the second geometry.  
      In other preferred embodiments the first robust geometry can be a cube, building shaped, a disk, or icosahedron; the second robust geometry can be a stellated cube, car shaped, sun shaped, or a stellated icosahedron.  
      A few embodiments of interconvertible articles of the invention are illustrated in  FIGS. 8-15 . In general, the interconvertible articles of the invention comprise a plurality of soft, resilient members that are interconnected at specific edges by hinge-type connections. Certain of the soft, resilient members are designed to be rotated 180 degrees (“rotatable members”). These rotatable members define an interior surface (“interconverting interior surface”). When the rotatable members are concomitantly rotated 180 degrees, the article interconverts such that the interconverting interior surface becomes the exterior surface (“interconverting exterior surface”). Because the interconverting interior and exterior surfaces can be designed such that they have substantially different geometries, colors, and textures, an exciting visual effect accompanies interconversion. To allow room for interconversion, certain soft, resilient members are unconnected at particular edges. Such unconnected edges define an “interconversion opening”. Pulling the soft, resilient members at the interconversion opening initiates interconversion, whereby a first robust geometry “snaps” to a second robust geometry. The snapping effect results from the potential energy generated by member distortion during interconversion. When the soft, resilient members are distorted, the potential energy generated tends to impel them back to their original shape. They can achieve their original shape by assuming a position consistent with either the article&#39;s first or second geometry. Beyond a “transition point” the article&#39;s second geometry is favored and the potential energy of distortion is released as the soft, resilient member assumes the second position consistent with the article&#39;s second geometry. After each rotating member assumes the second position, the interconversion is complete, and the resilient members return to their undistorted shapes.  
     5.2 Stability Concerns and Design Criteria  
      There are four main design criteria necessary to the creation of a robust, interconvertible toy. These criteria are: 
          1) dividing the first geometry into a nested set of adjacent elements;     2) choosing an arrangement of hinges between those elements that result in a stable, robust geometry;     3) eliminating a small number of adjacent hinges to create a single, interconversion opening whose position and shape does not compromise the toy&#39;s robustness; and     4) choosing the elements in such a way that after pulling them through the interconversion opening, the new geometry is also robust and does not distort the shape of any individual element.        

      It is not always possible to satisfy all four concerns. For example, a sphere cannot be divided into a small number of elements without violating criteria four because some of the hinge lines would be curved, and such curves will be distorted after the rotation necessary for interconversion, or members will be compressed in the second geometry. An approximation to a sphere, such as a polygonal icosahedron, however, has linear edges, and satisfies all four criteria.  
      The arrangement of hinged elements to create stable and robust geometries is based on substantial mathematical and practical considerations. For example, the study of hinges and rotation is important for architectural space frames, protein folding and atomic glasses.  
      Arrangement of hinges is very important. To understand the importance of hinge selection and directions, consider  FIG. 13 . Object  131 , consisting of members  1311 ,  1312  and hinges  1301 ,  1302  is very floppy and flexible. Note this is true whether the hinges are parallel or perpendicular. The hinge  1301  can rotate through almost 360 degrees, and is called “unconstrained”. On the other hand, object  132  consisting of members  1322 ,  1323 ,  1324  and three hinges  1303 , 1304  and  1305  is rigid and robust. The structure is stiff because three hinges are shared by one vertex, the hinges connect common members, and all three hinges do not lay in a plane. This arrangement is the physical realization of an elementary geometrical fact—to locate a plane in space, three coordinates are required. A similar effect is understood by house framers when building roof trusses, or by the designers of tents and tent poles.  
      Robustness depends on the hinges constraining common members from relative motion. In object  133  of  FIG. 7 , five members are connected by four hinges at a common vertex  1399 . But, because there is a gap between  1375  and  1371 , object  133  can flop over and lay flat. By traveling in a circle around vertex  1399  from  1371 , over hinge  1381 , to  1372  etc it is clear this transit will not return to  1371 , and thus is unconstrained. However, in  132  of  FIG. 7 , a transit around vertex  1366  shows all three hinges to be constraining, and thus this part of the object is robust.  
      Preferably, in articles of the invention, the members linked by constrained hinges. For example, in the cube of  FIG. 8A , there are five vertices each with 3 constrained hinges. Since each member is attached to at least one vertex with rigid, constrained hinges, the entire object is constrained and not floppy.  
      Thus, with respect to hinges, there are two guides for robustness: 
          1) in either interconverted geometry, the members cannot be distorted or under pressure; and     2) every interconverting member should be stabilized by at least one group of three or more constrained hinges attached along one edge.        

      One of skill in the art, by reference to the drawings and description herein and the above guides for robustness, can design a wide variety of interconvertible articles of the invention by providing a shell of soft, resilient material having exterior and interior surfaces of desired design; dividing the shell into soft, resilient members; and interconnecting the soft, resilient members with hinge-type connections such that appropriate soft, resilient members can be concomitantly rotated 180 degrees, and assuring each member is attached with constrained hinges. Typically, one begins by considering the most compact state (e.g. a solid cube) and then divides the solid body into a multitude of elements (e.g. pyramids) with common edges on the hinge lines. The larger the apparent volume and shape change, and the greater fraction of surface area interchanged, the more fascinating the transition.  
       FIGS. 8A-8C  illustrate an article of the invention  1 , which can be interconverted from robust cube geometry  1   a  ( FIG. 8A ) to robust faceted-ball geometry  1   b  ( FIG. 8C ). As shown in the exploded view of faceted-ball geometry  1   b  ( FIG. 9B ), article  1  is constructed of six pyramidal-shaped soft, resilient members  2 . As shown in  FIG. 9B , faceted-ball geometry  1   b  defines cube-shaped interior volume  3 . Referring to  FIG. 9B , the six members  2  are interconnected at edges  4  via hinge-type connections  5 . For simplicity, only one hinge-type connection  5  is shown in the drawing; however, edges  4  having hinge-type connections  5  are designated as broken lines in  FIG. 9 . All of the six members  2  are hinged at each of their four edges  4  (some hinged edges are not shown due to the limitations of the perspective drawing) except for member  2   a , which, is hinged on just two of its four edges (see  FIG. 2B , there are no hinge-type connections at edges  4   a  and  4   b  as indicated by the use of solid rather than hinge-indicating broken lines), thereby defining interconversion opening  7  ( FIG. 8B ). Article  1  is interconverted from cube geometry  1   a  to faceted-ball geometry  1   b , having twenty four triangular faces  8 , by rotation of each of the six members  2  via the hinge-type connections  5 . Mathematicians refer to geometry  1   b  as a stellated cube. Interconversion is accomplished, as illustrated in  FIG. 8B , by pulling member  2   a  outward and concomitantly pushing corner  9  upward. Note that the members  2  are the same pyramidal shape in both geometries  1   a  and  1   b . In geometry  1   b , the pyramidal bases  10  face inward defining an interconvertible interior surface area (i.e., the sum surface area of the six bases  10 ). This interconverting interior surface defines interior volume  3 , which is a hollow space of about the same volume as the first geometry  1   a . Upon interconversion to faceted ball  1   b , the outer dimension of the interconvertible cube  1   a  roughly doubles. When the bases  10  of the pyramidal members  2  are colored red, while the triangular sides are colored blue and made of artificial fur, the rapid switch in shape, size, color, and texture upon interconversion is both astonishing and entertaining. The article is useful as a toy, magician&#39;s prop, educational aid, ball, and even as a storage container, due to its high mechanical stiffness in either geometry.  
       FIGS. 10A-10C  illustrate another embodiment of the invention, article  10 , which can be interconverted from robust building geometry  10   a  to robust car geometry  10   b . As shown in  FIG. 11 &#39;s exploded view of car-geometry  10   b , article  10  is constructed from the five soft, resilient members  11  ( 11   a ,  11   b ,  11   c ,  11   d , and  11   e ). Hinge-type connections  12  at interconnecting edges  13  interconnect the five members  11 . In  FIG. 11 , broken lines indicate edges  13  that are interconnected by hinge-type connections  12 , while solid lines indicate edges  13  that are not interconnected. The appropriate edges are unconnected to define interconversion opening  14  ( FIGS. 10A and 10B ). Note that due to the perspectives limitations, some edges  13  are not shown. Article  10  is interconverted from building geometry  10   a  to car geometry  10   b  by rotating members  11   a ,  11   b ,  11   c , and  11   e  via the hinge-type connections  12 . Initiation of this interconversion is illustrated in  FIG. 10B  where the arrows indicate the direction of member rotation. As shown in  FIG. 10B , the user may interconvert article  11  by pulling members  11   a  and  11   e  outward and concomitantly pushing down on member lid. Article  10  can be decorated as desired, for example, with decorative wheels  15 . Both of geometries  10   a  and  10   b  are quite stiff and suited for robust play. Indeed, the robustness makes the interconversion surprising.  
       FIGS. 12A-12C  and  6  illustrate a third embodiment of the invention, article  20 , which can be interconverted from robust disk geometry  20   a  to robust sun geometry  20   b . As shown in the exploded view of  FIG. 13 , article  20  is constructed from the ten soft, resilient falcate-shaped members  21 , circular fabric band  22 , and disk-shaped member  23 . As shown in  FIG. 13 , in conformation  20   a , the four back edges  24  of each of soft, resilient members  21  are adjacent to the inside of circular fabric band  22 , which in turn is attached to disk-shaped member  23  via hinge-type connection  25 . Article  20  is interconverted from disk geometry  20   a  to sun geometry  20   b  by rotation of each of members  21  via hinge-type connection  25 , whereupon, circular fabric strip  22  folds over and contacts the outer circumference  26  of disk-shaped member  23 . As illustrated in  FIG. 12B , this is accomplished by pulling members  21  upward and over via interconversion opening  27 .  
       FIGS. 14A-14C  and  15  illustrate an article of the invention  30 , which can be interconverted from robust icosahedron geometry  30   a  ( FIG. 14A ) to robust stellated icosahedron geometry  30   b  ( FIG. 14C ). As shown in the exploded view of stellated icosahedron geometry  30   b  ( FIG. 15 ), article  30  is constructed of twenty triangular-based pyramid-shaped soft, resilient members  31  and, in stellated icosahedron geometry  30   b , defines icosahedron-shaped interior volume  32 . The twenty members  31  are interconnected at the edges of their triangular bases  33  via hinge-type connections  34 . For simplicity, only one hinge-type connection is shown in the drawing, however, edges  33  having hinge-type connections  34  are designated as broken lines in  FIG. 15 . All of the twenty members  31  are hinged at each of their three triangular base edges  33  (some hinged edges are not shown due to the limitations of the perspective drawing) except for adjacent members  31   a  and  31   b  (see  FIGS. 14A and 14B ), which, are hinged on just one of their respective edges  33  thereby defining interconversion opening  36  ( FIG. 14B ). Interconversion opening  36  is sufficient to allow interconversion and does not compromise stability of either geometry  30   a  or  30   b . Article  30  is interconverted from icosahedron geometry  30   a  to stellated icosahedron geometry  30   b , having twenty-four triangular faces  35  ( FIG. 14B ), by rotation of each of the twenty members  31  via the hinge-type connections  35 . Interconversion is accomplished, as illustrated in  FIG. 8B , by pulling members  31   a  and  31   b  of interconversion opening  36  outward and concomitantly pushing the opposite corner upward. Note that the members  31  are in the same triangular-based pyramidal shape in both geometries  30   a  and  30   b . In geometry  30   b , the triangular bases  35  face inward defining an interconvertible interior surface area. This interconverting interior surface defines volume  32 , which is a hollow space of about the same volume as the first geometry  30   a . Upon interconversion of  30   a  to  30   b , the outer dimension of article  30  roughly doubles. Stunning effects can be achieved by color and texture differences between the triangular sides and bases.  
      The articles of the invention may be decorated in any manner, for example, in article  10 , car windows, wheels  15 , etc. can be added to the car surface, while windows, doors, etc. can be added to the building surface.  
      The foregoing description of non-limiting embodiments of the invention has been presented for illustrative purposes. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and many modifications and variations are possible in light of the above teachings without deviating from the spirit and the scope of the invention. The embodiments described are selected to illustrate the principles of the invention and its practical application to thereby enable others skilled in the art to practice the invention in various embodiments and with various modifications as suited to their particular purpose.