All Questions

Two students in my class asked and answered what might be a novel question. It is well known that the cube has exactly $11$ edge-unfoldings (or "nets"), as shown below:         (Image from ...

Encouraged by the positive solutions to my question, Tiling with one of each shape, I'd like to pose the $\mathbb{R}^3$ equivalent: Q. Is there a tiling of $\mathbb{R}^3$ by (bounded) polyhedra, one ...

A 4-dimensional cross-polytope (also called 16-cell) is a regular polytope whose vertices are all permutations of $(\pm1,0,0,0)$. It is known that this body tiles the space $\mathbb{R}^4$ by ...