Hideki Tsuiki: Imaginary Cube Puzzles

An imaginary cube is a three-dimensional object which has square projections in three orthogonal directions, just like a cube has.   How many different imaginary cubes can you imagine?  In this talk, I show some mathematics about imaginary cubes and present puzzles and mathematical sculptures based on them.   I have a copy of the "Fractal Sudoku Sculpture" in order to share its beauty with the audience. You can enjoy the puzzle "3H=6T" before/after the talk.

The following four are typical examples of imaginary cubes. Can you explain why they are imaginary cubes (see enclosed PDF file)?

1. regular tetrahedron
2. cuboctahedron
3. H: hexagonal bipyramid with twelve isosceles triangle faces with the height 3/2 of the base,
4. T: triangular antiprismoid obtained by truncating the three vertices of a base of a regular triangular prism whose height is √6/4 of an edge.