The Dice Lab space filling dice page

Space-Filling Dice

A space-filling polyhedron is a three-dimensional shape with polygonal faces that will tile three-dimensional space without leaving gaps. The simplest example is a cube, which is the polyhedron commonly used for d6 dice. The Dice Lab d8 (truncated octahedron) and d12 (rhombic dodecahedron) dice are also space fillers, as shown below.

Stacked d8 dice
Truncated Octahedral d8

Stacked d12 dice
Rhombic Dodecahedral d12