# Yasuyuki Tsukamoto and Hideki Tsuiki

"Imaginary Cube" is a simple geometrical idea; it is an object which has three square projections just as a cube has. Based on the mathematical studies of imaginary cubes, the authors designed sculptures and puzzles, and find way to use them for mathematical education from elementary schools up to universities. For mathematical side, please see the papers in Bridges proceedings 2007 and 2010. Among the sculptures, is this one full of mathematics, beauty, playful spirit, and craftsmanship. It is compact and robust enough to be carried to workshop classes. The classes are always filled with a sense of wonder when this object forms a flat square shadow on a screen.

This is a remake of

"Hexagonal Bipyramid Fractal with a SUDOKU coloring"

http://www.bridgesmathart.org/art-exhibits/bridges2007/tsuiki.html

presented at Bridges 2007 to a portably sized object.

This pre-fractal shape consists of 81 hexagonal bipyramid pieces and has many beautiful appearances. In particular, it is projected to a square in 6 different ways, in each of which it has a 9x9 grid appearance. The 81 pieces are painted in nine colors so that they form a SUDOKU solution pattern in each of the square projections. The previous one was rather big, fragile, and, imprecise. This one is compact, robust, and assembled carefully with high precision. It has been used for a lot of workshop classes.