pieces, there are 48 selections of S(6,6) = 462 possible
selections (definition parts 1,2,3) that provide the necessary
12 male and 12 female keys exactly. Of these 48 selections, 8
provide the proper quantity of 8, intrinsically included,
corner pieces (definition parts 1,2,3,4), while the other 40
selections can be adjusted to 8 corners, in many different
ways, by adding or subtracting corners (definition parts 5,6)
to form the shell perfectly.
The puzzle pieces derived from the above set definition,
parts 1,2,3, & 4 for the normal-edge dissection of a
tetrahedron shell, FIG. 4, are shown in outline, FIG. 5.
Extending the definition to parts 5 & 6, there would be 17
pieces in all. From S(4,4) = 35 selections of pieces, there
are 5 that provide the necessary 6 male and 6 female keys
exactly, and only one that intrinsically includes the proper
quantity of 4 corner pieces exactly, that selection being the
four outlined pieces K,L,M, and N of FIG. 5.
An important property of a well defined set of sectioned
shell puzzles is that the derived pieces be capable of
building shells of different size and shape than that of the
original dissection. The cube shell pieces are extremely apt
in this respect and a large quantity of puzzle pieces can
constitute a construction block toy. However many larger built
shells could readily collapse. To prevent collapse, the pieces
have binding holes, indicated on the pieces of FIG. 2 by the
small circles, and can be secured together in the same and at
intersecting planes by tapered binding pins, FIG. 3. In
addition to the defined dissection puzzle pieces, a
construction block toy can also include a variety of other
blocks such as face, edge, and corner pieces of the
dissection, as well as posts, columns, partians, doors,
stairs, etc.. These additional pieces would also have binding
holes and their combination with a large set of puzzle pieces
produces a block toy having extensive scope of design. Cube
block pieces, buildable in many imaginative ways, can also be
combined in many strange and interesting offset patterns.
The regular shells of the five regular polyhedron solids all
yield fascinating normal-edge dissection puzzles. Of these,
the tetrahedron is the simlest puzzle and the cube the most
intriguing construction block toy. Every other polyhedron
shell has a unique normal-edge dissection and an interlocking
planar puzzle piece set, but, for the most part, the derived
pieces fit together in few ways and are unable to build
differently shaped shells extensively.
In the foregoing definition of sectioned shell puzzles only
1 male or 1 female key is provided to the edges of planar
puzzle pieces. Shell edge pieces could also be sectioned into
any number of parts, in many different ways, to provide any
number of keys, in any combination, to the edges of shell face
pieces. Special or offset keying can limit the number of ways
proper piece selections can be combined perfectly, but, in
general, multi-keyed pieces have an unpleasing, unnecessarily
Many various materials can be used to compose the pieces of
puzzles and construction block toys. Pieces can be
transparent, colored, or opaque. The puzzle container itself
can be a piece or pieces of the puzzle. Pieces could also have
designs or further sectioned parts, holes, or patterns, not
directly related to the normal-edge or the abnormal-edge
polyhedron shell dissection.
Having set forth disclosure of my invention, I claim:
1. A puzzle comprising a finite number of puzzle pieces of
a normal edge dissection of a polyhedron shell, wherein
selections of said pieces can be fit together to form the
original polyhedron shell perfectly, each of said pieces being
planar and comprising an entire face of said polyhedron shell,
each piece at each edge thereof having either a centrally
located male edge key with female edge keys on opposite sides
thereof or a centrally located female edge key with male edge
keys on opposite sides thereof, and each piece further
including at each corner a male or a female key, a said
selection of said pieces being equal in number to the number
of faces of a given polyhedron to form the faces thereof, with
the male and female edge keys of said selected pieces together
forming the given polyhedron edges perfectly, and with the
male and female corner keys of said selected pieces together
forming the corners of the given polyhedron perfectly.
2. The puzzle of claim 1 where the section locations of the
edge piece part dissection number two and are located at the
interior end points of 3 equal edge segments of every exterior
shell edge; and where every exterior shell edge is greater in
length than 3 times the uniform shell thickness.
3. The puzzle of claim 1 where the section locations of the
edge piece part dissection number two and are located anywhere
on the exterior edges of shell edge pieces.
4. The puzzle of claim 1 where the section locations of the
edge piece part dissection are any number 2 or more and are
located anywhere on the exterior edges of shell edge pieces;
and where plural edge keys are provided to each edge of each
piece in a manner similar to the single-keyed pieces.
5. The puzzle of claim 1 where the exterior edges of said
polyhedron shell all have the same length.
6. The puzzle of claim 5 where said polyhedron shell is a
7. The puzzle of claim 5 where said polyhedron shell is a
8. The puzzle of claim 1 where a finite number of said
puzzle pieces provides selections of said pieces that are able
to build shells of different size and shape than that of the
original dissection and constitute a construction block toy.
9. The construction block toy of claim 8 where said pieces
have binding holes sectioned therein and there are binding
pins capable of engaging the binding holes to secure pieces
together in the same and at intersecting planes.