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The triangular prismatic honeycomb or triangular prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed entirely of triangular prisms.
Contents
- Hexagonal prismatic honeycomb
- Trihexagonal prismatic honeycomb
- Truncated hexagonal prismatic honeycomb
- Rhombitrihexagonal prismatic honeycomb
- Snub hexagonal prismatic honeycomb
- Truncated trihexagonal prismatic honeycomb
- Elongated triangular prismatic honeycomb
- Gyrated triangular prismatic honeycomb
- Gyroelongated triangular prismatic honeycomb
- References
It is constructed from a triangular tiling extruded into prisms.
It is one of 28 convex uniform honeycombs.
Hexagonal prismatic honeycomb
The hexagonal prismatic honeycomb or hexagonal prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of hexagonal prisms.
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).
Trihexagonal prismatic honeycomb
The trihexagonal prismatic honeycomb or trihexagonal prismatic cellulation is a space-filling tessellation (or honeycomb) 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 (or honeycomb) 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 (or honeycomb) 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.
Snub hexagonal prismatic honeycomb
The snub hexagonal prismatic honeycomb or simo-trihexagonal prismatic cellulation is a space-filling tessellation (or honeycomb) 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 hexagonal 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 (or honeycomb) 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.
Elongated triangular prismatic honeycomb
The elongated triangular prismatic honeycomb or elongated antiprismatic prismatic cellulation is a space-filling tessellation (or honeycomb) 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 (or honeycomb) 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 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.
Gyroelongated triangular prismatic honeycomb
The gyroelongated triangular prismatic honeycomb or elongated parasquare fastigial cellulation is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of cubes and triangular prisms in a ratio of 1:2.
It is created by alternating laters 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.