Amusement devices: games – Puzzles – Take-aparts and put-togethers
Reexamination Certificate
1999-07-19
2001-07-24
Wong, Steven (Department: 3711)
Amusement devices: games
Puzzles
Take-aparts and put-togethers
C273S155000
Reexamination Certificate
active
06264199
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates to transformational folding puzzle assemblies, and, more particularly, to a transformational ring of 24 isosceles tetrahedrons which can be used for educational, entertainment, or advertising purposes.
Rings of rotating tetrahedrons have been known for many years. The earliest known relevant patent, U.S. Pat. No. 1,997,022 to Stalker in 1933, presented the original use for such rings as an advertising medium or toy. While it mentions larger tetrahedron rings, the preferred embodiment (pictured in the patent) is a ring of six or eight isosceles tetrahedrons. The concept is described in Ball & Coxeter,
Mathematical Recreations and Essays,
along with an arrangement of the numbers from 1 to 32 by Heath on “a magic rotating ring” of eight regular (not isosceles) tetrahedra. Doris Schattschneider and Wallace Walker copyrighted various isosceles tetrahedron rings of 6 to 12 members which they covered with M. C. Escher tessellated patterns and termed them kaleidocycles. The entertainment value of Stalker's assembly and Walker/Schattschneider's rings involve the visual appearance and transformation of colors and images when the connected bodies are simultaneously rotated upon their individual axes (at opposite edges of the ring towards the center) to bring disparate surfaces into edge-adjacent, abutting relationship. For this particular effect it is important to have less tetrahedra (the minimum for a tetrahedron ring is six), generally six to eight.
Rings of tetrahedra that are meant to be “flipped and folded” to make solid geometrical shapes, rather than to make changing patterns, are also Unavailable. One such manifestation, made out of cloth hinges and plastic tetrahedrons features two colors and 12 irregular right tetrahedrons. Depicted on the descriptive packaging for this product are about 18 shapes that can be made by folding up the ring. The only graphic differentiation between the triangular paces of the tetrahedrons is that they come in two different colors. No means of holding the shapes together is given; in general the arrangements are held together simply by the inertial weight of the plastic tetrahedrons upon one another.
A major disadvantage of the prior art in relation to rotating tetrahedron rings concerns this separation between the two methods of designing tetrahedron rings. If the only effect desired from a rotating tetrahedron ring is the kaleidoscopic effect of different faces tumbling in towards the center of the ring as the ring is rotated about its closed loop axis, then the most important factor is that each of the four triangular faces of each tetrahedron in the ring be graphically different (either in color or design) and that the ring be of small size (6 to 12 tetrahedrons) so this effect can be easily seen. If the primary effect desired from a tetrahedron ring is that it contract to form various random solid shapes, the most important factor is that the tetrahedrons be “allspace-filling”, so that there are no irregular gaps or voids between or among the surfaces of the contracted shape, and that the ring be of large size (12 or more tetrahedrons).
Prior art involving the arrangement of magic numbers on the surface of a rotating tetrahedron ring has several disadvantages. The only described version (Heath) has only one true connection with exterior shape, which is that there is a magic constant (the sum of all four triangles) for each tetrahedron contained on the ring. Other magic constants he describes involve tracing out patterns mentally as the viewer travels in a spiral fashion around the ring. Heath's version (published in Ball & Coxeter, Mathematical Recreations and Essays, p. 216) is depicted as consisting of equilateral triangles and makes a ring of eight regular tetrahedrons. It is a geometric fact that the regular tetrahedron is not an all-space filling tetrahedron. Thus this prior art “magic number” ring necessarily belongs to the category of tetrahedron rings which are meant to rotate towards the center and cannot be contracted into coherent solid shapes with no gaps between the tetrahedrons. Therefore, while Heath suggests a number of magic constants of greater magnitude than the sum of the triangles on every tetrahedron, none of them are related to a larger, contracted, all-space filling shape.
Accordingly, it would be desirable to have a rotating tetrahedron ring that has:
1) sufficient size to use the capacity of all-space filling tetrahedrons to be grouped to form a large plurality of geometric solid-shapes; and,
2) sufficient graphic intricacy involved in the color/design/arrangement of the triangular faces such that, at a minimum, each contracted shape has at least four visually distinct representations. In addition it would be desirable that in order to fully explore the potentials of the relationship between design and shape, that the shape be held together in such a way that it does not come apart when it is picked up. Accordingly an external or internal means should be provided for holding the tetrahedron ring together in various contracted shape configurations.
SUMMARY OF THE INVENTION
The present invention generally comprises a transformational folding puzzle assembly formed of a chain or ring of 24 isosceles tetrahedrons. The tetrahedrons are identical in configuration, and are all-space filling. One aspect of the invention is to combine the hitherto separate properties of tetrahedron rings, i.e., rotatability as a ring and contractility to form solid shapes, such that the contracted solid shape and the color/design of the faces are intimately related in order to make an entertaining toy, puzzle, educational, or novelty item. Depending on decoration and manipulation, it is capable of forming a variety of puzzles involving shapes, figures, and numbers; in addition, a plurality of such toys can be made into both large and small scale construction sets.
Another object of the invention is to go beyond the prior art by exploiting properties of the tetrahedral ring and solid shapes formed thereby that were heretofore undiscovered. For example, the invention provides: 1) the construction of a great variety of new shapes, more than a hundred with diamond faces and hundreds more without that limitation; 2) A variety of shape dependent puzzles including a novel family of geometric transformational magic shapes; 3) a transformational four year calendar/ball in which the twelve months of the year are expressed on the 12 diamond faces of the ball exteriorly while the other three years are hidden in the interior of the rhombic dodecahedron ball; 4) a means of holding the shapes together and of attaching them to one another, allowing for a construction set in which each piece can transform into hundreds of other possible pieces.
These objects are achieved by a ring (endless loop) or broken ring (chain) made up of 24 interconnected isosceles tetrahedrons. This invention incorporates unique physical properties of such a ring or chain, as follows. When a suitable arrangement of four different colors for the four different faces of each tetrahedron is given, the ring may be contracted into four distinguishable rhombic dodecahedron balls, each ball having a different, solid exterior color. In addition, if each of the twelve diamond faces on the exterior surface of the contracted rhombic dodecahedron balls is provided with a predetermined display of the day arrangement for a month, a four year calendar can be created with each of the four contracted dodecahedron ball arrangements representing one calendar year.
Alternatively, if the 96 triangles of the 24 tetrahedrons are covered with a predetermined arrangement of the numbers from 1 to 96, the numbers on each separate rhombic dodecahedron surface will add up to the same magic constant: 1164. Further play possibilities can involve discovering the other different shapes which have the same property of adding up to the same numerical constant, as well as investigating the possibility of other numerical constants involved in various sh
Cohen Howard
Wong Steven
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