| bgcolor=#e7dcc3 colspan=2 | Triangular prismatic honeycomb | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | ||
| Type | Uniform honeycomb | |
| Schläfli symbol | × or t0,3 | |
| Coxeter diagrams | ||
| Space group Coxeter notation | [6,3,2,∞] [3<sup>[3],2,∞] [(3<sup>[3])+,2,∞] | |
| Dual | Hexagonal prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from a triangular tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
It consists of 1 + 6 + 1 = 8 edges meeting at a vertex, There are 6 triangular prism cells meeting at an edge and faces are shared between 2 cells.
| bgcolor=#e7dcc3 colspan=2 | Hexagonal prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Schläfli symbols | × or t0,1,3 | |
| Coxeter diagrams | ||
| Cell types | 4.4.6 | |
| Vertex figure | triangular bipyramid | |
| Space group Coxeter notation | [6,3,2,∞] [3<sup>[3],2,∞] | |
| Dual | Triangular prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from a hexagonal tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
This honeycomb can be alternated into the gyrated tetrahedral-octahedral honeycomb, with pairs of tetrahedra existing in the alternated gaps (instead of a triangular bipyramid).
There are 1 + 3 + 1 = 5 edges meeting at a vertex, 3 Hexagonal Prism cells meeting at an edge, and faces are shared between 2 cells.
| bgcolor=#e7dcc3 colspan=2 | Trihexagonal prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Schläfli symbol | rx or t1,3x | |
| Vertex figure | Rectangular bipyramid | |
| Coxeter diagram | ||
| Space group Coxeter notation | [6,3,2,∞] | |
| Dual | Rhombille prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from a trihexagonal tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
| bgcolor=#e7dcc3 colspan=2 | Truncated hexagonal prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Schläfli symbol | t× or t0,1,3 | |
| Coxeter diagram | ||
| Cell types | 4.4.12 3.4.4 | |
| Face types | , , | |
| Edge figures | Square, Isosceles triangle | |
| Vertex figure | Triangular bipyramid | |
| Space group Coxeter notation | [6,3,2,∞] | |
| Dual | Triakis triangular prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from a truncated hexagonal tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
| bgcolor=#e7dcc3 colspan=2 | Rhombitrihexagonal prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Vertex figure | Trapezoidal bipyramid | |
| Schläfli symbol | rr× or t0,2,3 s2× | |
| Coxeter diagram | ||
| Space group Coxeter notation | [6,3,2,∞] | |
| Dual | Deltoidal trihexagonal prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from a rhombitrihexagonal tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
| bgcolor=#e7dcc3 colspan=2 | Truncated trihexagonal prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Schläfli symbol | tr× or t0,1,2,3 | |
| Coxeter diagram | ||
| Space group Coxeter notation | [6,3,2,∞] | |
| Vertex figure | irr. triangular bipyramid | |
| Dual | Kisrhombille prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from a truncated trihexagonal tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
| bgcolor=#e7dcc3 colspan=2 | Snub trihexagonal prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Schläfli symbol | sr× | |
| Coxeter diagram | ||
| Symmetry | [(6,3)<sup>+</sup>,2,∞] | |
| Dual | Floret pentagonal prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from a snub trihexagonal tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
| bgcolor=#e7dcc3 colspan=2 | Snub trihexagonal antiprismatic honeycomb | |
|---|---|---|
| Type | Convex honeycomb | |
| Schläfli symbol | ht0,1,2,3 | |
| Coxeter-Dynkin diagram | ||
| Cells | hexagonal antiprism octahedron tetrahedron | |
| Vertex figure | ||
| Symmetry | [6,3,2,∞]+ | |
| Properties | vertex-transitive |
| bgcolor=#e7dcc3 colspan=2 | Elongated triangular prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Schläfli symbols | e× | |
| Coxeter diagrams | ||
| Space group Coxeter notation | [∞,2<sup>+</sup>,∞,2,∞] [(∞,2)<sup>+</sup>,∞,2,∞] | |
| Dual | Prismatic pentagonal prismatic honeycomb | |
| Properties | vertex-transitive |
It is constructed from an elongated triangular tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
| bgcolor=#e7dcc3 colspan=2 | Gyrated triangular prismatic honeycomb | |
|---|---|---|
| Type | Convex uniform honeycomb | |
| Schläfli symbols | g× | |
| Cell types | (3.4.4) | |
| Face types | ||
| Vertex figure | ||
| Space group | [4,(4,2<sup>+</sup>,∞,2<sup>+</sup>)] ? | |
| Dual | ? | |
| Properties | vertex-transitive |
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 create gyrobifastigium cells. 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.
| bgcolor=#e7dcc3 colspan=2 | Gyroelongated triangular prismatic honeycomb | |
|---|---|---|
| Type | Uniform honeycomb | |
| Schläfli symbols | ge× | |
| Vertex figure | ||
| Space group Coxeter notation | [4,(4,2<sup>+</sup>,∞,2<sup>+</sup>)] ? | |
| Dual | - | |
| Properties | vertex-transitive |
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: