The trihexagonal prismatic honeycomb or trihexagonal prismatic cellulation is a space-filling tessellation in Euclidean 3-space. It is composed of hexagonal prisms and triangular prisms in a ratio of 1:2. It is constructed from a trihexagonal tiling extruded into prisms. It is one of 28 convex uniform honeycombs.
Truncated hexagonal prismatic honeycomb
The truncated hexagonal prismatic honeycomb or tomo-trihexagonal prismatic cellulation is a space-filling tessellation in Euclidean 3-space. It is composed of dodecagonal prisms, and triangular prisms in a ratio of 1:2. It is constructed from a truncated hexagonal tiling extruded into prisms. It is one of 28 convex uniform honeycombs.
Rhombitrihexagonal prismatic honeycomb
The rhombitrihexagonal prismatic honeycomb or rhombitrihexagonal prismatic cellulation is a space-filling tessellation in Euclidean 3-space. It is composed of hexagonal prisms, cubes, and triangular prisms in a ratio of 1:3:2. It is constructed from a rhombitrihexagonal tiling extruded into prisms. It is one of 28 convex uniform honeycombs.
Truncated trihexagonal prismatic honeycomb
The truncated trihexagonal prismatic honeycomb or tomo-trihexagonal prismatic cellulation is a space-filling tessellation in Euclidean 3-space. It is composed of dodecagonal prisms, hexagonal prisms, and cubes in a ratio of 1:2:3. It is constructed from a truncated trihexagonal tiling extruded into prisms. It is one of 28 convex uniform honeycombs.
The snub trihexagonal prismatic honeycomb or simo-trihexagonal prismatic cellulation is a space-filling tessellation in Euclidean 3-space. It is composed of hexagonal prisms and triangular prisms in a ratio of 1:8. It is constructed from a snub trihexagonal tiling extruded into prisms. It is one of 28 convex uniform honeycombs.
Snub trihexagonal antiprismatic honeycomb
A snub trihexagonal antiprismatic honeycomb can be constructed by alternation of the truncated trihexagonal prismatic honeycomb, although it can not be made uniform, but it can be given Coxeter diagram: and has symmetry+. It makes hexagonal antiprisms from the dodecagonal prisms, octahedra from the hexagonal prisms, tetrahedra from the cubes, and two tetrahedra from the triangular bipyramids.
The elongated triangular prismatic honeycomb or elongated antiprismatic prismatic cellulation is a space-filling tessellation in Euclidean 3-space. It is composed of cubes and triangular prisms in a ratio of 1:2. It is constructed from an elongated triangular tiling extruded into prisms. It is one of 28 convex uniform honeycombs.
Gyrated triangular prismatic honeycomb
The gyrated triangular prismatic honeycomb or parasquare fastigial cellulation is a space-filling tessellation in Euclidean 3-space made up of triangular prisms. It is vertex-uniform with 12 triangular prisms per vertex. It can be seen as parallel planes of square tiling with alternating offsets caused by layers of paired triangular prisms. The prisms in each layer are rotated by a right angle to those in the next layer. It is one of 28 convex uniform honeycombs. Pairs of triangular prisms can be combined to creategyrobifastigiumcells. The resulting honeycomb is closely related but not equivalent: it has the same vertices and edges, but different two-dimensional faces and three-dimensional cells.
Gyroelongated triangular prismatic honeycomb
The gyroelongated triangular prismatic honeycomb or elongated parasquare fastigial cellulation is a uniform space-filling tessellation in Euclidean 3-space. It is composed of cubes and triangular prisms in a ratio of 1:2. It is created by alternating layers of cubes and triangular prisms, with the prisms alternating in orientation by 90 degrees. It is related to the elongated triangular prismatic honeycomb which has the triangular prisms with the same orientation. This is related to a space-filling polyhedron, elongated gyrobifastigium, where cube and two opposite triangular prisms are augmented together as a single polyhedron:
