Equiprojective Polyhedra

Definitions and mathematical statement

Shared notation.

$\mathbb N=\{1,2,\ldots\}$, and $\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$ denote the integers, rationals, reals and complex numbers. Any other conventions are specified locally.

A polyhedron is $k$-equiprojective when orthogonal projection onto a plane gives a polygon with exactly $k$ sides for every projection direction not parallel to any face. The integer $k$ is independent of direction. For example, a cube is $6$-equiprojective.

Statement recorded in the supplied source.

Identify or construct all $k$-equiprojective polyhedra, for all possible integers $k$. [S2]

Short English statement

Identify or construct all $k$-equiprojective polyhedra, for all possible integers $k$.

Sources

• S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 5500076 (AMR-054-0076). CC BY 4.0. https://huggingface.co/datasets/ulamai/UnsolvedMath.
• S2 Erik D. Demaine, Joseph S. B. Mitchell and Joseph O'Rourke (editors), The Open Problems Project, maintained original source, Problem 76, Statement and complete Partial/Related Results. https://github.com/edemaine/topp/blob/main/Problems/P.000076.