# Bridges 2010 Regular Paper

Imaginary Cubes—Objects with Three Square Projection Images

Hideki Tsuiki

(Proceedings pages 159–166)

## Abstract

An imaginary cube is a three dimensional object which has square
projections in three orthogonal directions just as a cube has. In
this paper, we study imaginary cubes and present sculptures based
on imaginary cubes. We show that there are 16 kinds of minimal
convex imaginary cubes. The list of 16 representative minimal convex
imaginary cubes contains, as well as a regular tetrahedron and a
cuboctahedron, a hexagonal bipyramid imaginary cube, which is a
double imaginary cube, and a triangular antiprism imaginary cube,
which plays an important role in the construction of the sculptures.
Then, we present two Imaginary Cube Sculptures. Each of them is
composed of all the 16 representative minimal convex imaginary cubes
and forms an imaginary cube as a whole. Thus, they reveal uniform
overall structures though they are composed of different shapes.

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