Hexagonal tiling honeycomb tetrahedron vertex figure. The runcinated hexagonal tiling honeycomb, t{6,3,3}, has tetrahedron, rhombitrihexagonal tiling hexagonal prism, triangular prism cells, with a octahedron vertex figure. The runcitruncated hexagonal tiling honeycomb, t{6,3,3}, has cuboctahedron, Triangular prism, Dodecagonal prism, and truncated hexagonal tiling cells, with a quad-pyramid vertex figure. The runcicantellated hexagonal tiling honeycomb or runcitruncated order-6 tetrahedral honeycomb, t{6,3,3}, has truncated tetrahedron, hexagonal prism, hexagonal prism, and rhombitrihexagonal tiling cells, with a quad-pyramid vertex figure. The omnitruncated hexagonal tiling honeycomb or omnitruncated order-6 tetrahedral honeycomb, t{6,3,3}, has truncated octahedron, hexagonal prism, dodecagonal prism, and truncated trihexagonal tiling cells, with a quad-pyramid vertex figure.
Rectified tesseractic honeycomb Rectified tesseractic honeycomb In four-dimensional Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a rectification of a tesseractic honeycomb which creates new vertices on the middle of all the original edges, rectifying the cells into rectified tesseracts, and adding new 16-cell facets at the original vertices. Its vertex figure is an octahedral prism, {3,4}×{}. It is also called a quarter tesseractic honeycomb since it has half the vertices of the 4-demicubic honeycomb, and a quarter of the vertices of a tesseractic honeycomb. Regular and uniform honeycombs in 4-space: