The object of this puzzle is to assemble the 10 burrs as in the picture above to form a square lattice. The pieces collects all the possible combination of position of 5 notches laddered in a burr; where a notch can be at a face or the other face, and burrs are considered to be equivalent if they are congruent by reversing, rotating etc. The notches at both ends of burrs must be exposed so that to be constructable.
It was pointed out that the logic of this design is the same as "Pot Stand" by Nob. Yoshigahara. (In his design, the notches at both ends are not exposed, instead, it was made from rubber.)
This puzzle is presented at ISHINO, Keiichiro-san's site together with some of the other puzzles. He also informed me about Pot Stand by Nob. Yoshigahara. Thanks ISHINO-san. Moreover, it seems that "Strip Tease" by Maarten Vermaak (IPP-2002) has almost the same logic as this puzzle, though its physical construction is completely different. Vermaak's design is very impressive!
This puzzle consists of 8 equal sized cubes, where each cube is drawn 1 or 2 closed line on its surface with passing through midpoint of the edges, which collects all possible patterns. The object is to form a cube of 2 x 2 x 2 with matching lines on the surface and make them up single loop.
I was informed that this puzzle is equivalent with old English puzzle 'Python Puzzle'.
The object of the puzzle is to assemble 12 burrs to form a cubic cage. Conceptually, a burr's end can be one of 3 types, say, A, B and C, and a burr itself can be straight or twisted 90 degree. It turns out that there exists 12 kinds of burr; A-A, A-B, A-C, B-B, B-C, C-C and A+A, A+B, A+C, B+B, B+C, C+C (the sign indicates straight or twisted). The burrs of the puzzle collects all of these kinds as you can see in the first picture above. A construction of 3 ends of burrs at a vertex of the cage must consist of all 3 types; which can be one of 2 types, each of which enantiomorphic to the other ('left-hand' and 'right-hand'). Whether constructions at 2 adjacent vertices are enantiomorphic or isomorphic depends on the twisting of the burr connecting the vertices (isomorphic if twisted).
The design and crafting in the picture is rough and ready. Two designs given in the following figures may be more well polished. Since the design in the second figure contains one solid plain burr, it may have more constructable solutions than the first one (and actually, it does have).
Below is an excellent craft work made by Eric Fuller - product page) The work in the picture is a unique copy specially made for me which consists of 3 kinds of wood; thanks! Eric. This is truly accurate craft work which materialized both very little clearance and smoothness of construction.
The picture below illustrates a solution which is impossible to construct. Thus, one piece is not put in.
The object is to form a regular dodecahedron cage with 10 pieces shown in the first of the above pictures.
Pieces collects all possible assemble of vertices and edges of regular dodecahedron such that:
(1) a piece must consist of 2 vertices connected with an edge.
(2) a piece can have 0 through 4 edges (without counting the edge connecting the 2 vertices) connected to the 2 vertices.
For the pieces in the rightmost 3 columns of the above picture, the lower row is mirror image of the upper row.
Actually, the design above has a problem that it is awkward to construct the cage, since the connection of 2 vertices in the same piece is not flexible. Using magnets as connecters will make it ease (though one might need to label them so that S pole and N pole to be distinguishable).
Do not put it near hook-bills. They will panic.
In the above puzzle, the connections between 2 pieces are 'stick and hole'. If one change it to 'handshake' (i.e. the sticks and holes are replaced with right and left hands), another design will be made. The figure below illustrates a solution for each design. The left diagram illustrates the solution of former one and the right illustrates the latter one.
[Caution: Both this puzzle and the next puzzle 'Cubes + Squares' are impossible because of parity inconsistency.]
The object of the puzzle is, using 8 cubes and 6 tiles of 2x2 shown in the figure above, to form a cube of 2x2x2 and cover 6 faces of the cube with the 6 tiles, where every faces of 1x1 must match so that diagonal lines are orthgonal each other.
The physical design can be given as at lower right of the figure above.
Another puzzle will be made by using medians instead of using diagonal lines as given in the figure above. The logic is equivalent to the previous puzzle if diagonal lines are matched parallel.
Mr. Ishino informed me that the above 2 puzzles are impossible. He also informed me that there are 820800 (or 823680 for the latter one) solutions if one construct only a cube of 2x2. Huge number of solutions! Why imppossible? I thought that there must be a mathematical logic in it. And there exists. For me, it is very complicated to explain it here in English (learn Japanese...).