Honeycomb (geometry) From Wikipedia

Uniform honeycombs

A uniform honeycomb is a honeycomb in Euclidean 3-space composed of uniform polyhedral cells, and having all vertices the same (i.e. it is vertex-transitive or isogonal). There are 28 convex examples[1], also called the Archimedean honeycombs. Of these, just one is regular and one quasiregular:

  • Regular honeycomb: Cubes.
  • Quasiregular honeycomb: Octahedra and tetrahedra

Space-filling polyhedra[2]

A honeycomb having all cells identical within its symmetries is said to be cell-transitive or isochoric. A cell is said to be a space-filling polyhedron. Well-known examples include:

A dodecahedral honeycomb in hyperbolic space