Rhombic dodecahedral honeycomb cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing. The "rhombic dodecahedral honeycomb" can be dissected into a trigonal trapezohedral honeycomb with each rhombic dodecahedron dissected into 4 trigonal trapezohedrons. Each rhombic dodecahedra can also be dissected with a center point into 12 rhombic pyramids of the rhombic pyramidal honeycomb. The trapezo-rhombic dodecahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It consists
2 22 honeycomb types of cells: octahedron, 0, and tetrahedron, 0. The 2 honeycomb, is fourth in a dimensional series of uniform polytopes, expressed by Coxeter as k series. The final is a paracompact hyperbolic honeycomb, 3. Each progressive uniform polytope is constructed from the previous as its vertex figure. The 2 honeycomb is third in another dimensional series 2. 2 22 honeycomb In geometry, the 2 honeycomb is a uniform tessellation of the six-dimensional Euclidean space. It can be represented by the Schläfli symbol {3,3,3}. It is constructed from 2 facets and has a 1 vertex figure, with 54 2 polytopes around