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:
- The regular packings[3] of cubes, hexagonal prisms, and triangular prisms.
- The uniform packing of truncated octahedra[4].
- The rhombic dodecahedral honeycomb. [5]
- The squashed (rhombic) dodecahedron honeycomb [6].
- The rhombo-hexagonal dodecahedron honeycomb [7].
- A packing of any cuboid, rhombic hexahedron or parallelepiped.
A dodecahedral honeycomb in hyperbolic space
http://en.wikipedia.org/wiki/Honeycomb_%28geometry%29
