| Octahedral prism | |
|---|---|
Schlegel diagram |
|
| Type | Prismatic uniform polychoron |
| Uniform index | 51 |
| Schläfli symbol | {3,4}x{} t1{3,3}x{} s{2,3}x{} |
| Coxeter-Dynkin | |
| Cells | 2 (3.3.3.3) 8 (3.4.4) |
| Faces | 16 {3}, 12 {4} |
| Edges | 30 |
| Vertices | 12 |
| Vertex figure | Square pyramid |
| System groups | [3,4,2], order 96 [3,3,2], order 48 [(3,2)+,2], order 12 |
| Properties | convex |
In geometry, a octahedral prism is a convex uniform polychoron (four dimensional polytope). This polychoron has 10 polyhedral cells: 2 octahedra connected by 8 triangular prisms.
Contents |
It is the first in an infinite series of uniform antiprismatic hyperprisms.
It is one of 18 uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids and Archimedean solids.
The octahedral prism consists of two octahedra connected to each other via 8 triangular prisms. The triangular prisms are joined to each other via their square faces.
The octahedron-first orthographic projection of the octahedral prism into 3D space has an octahedral envelope. The two octahedral cells project onto the entire volume of this envelope, while the 8 triangular prismic cells project onto its 8 triangular faces.
The triangular-prism-first orthographic projection of the octahedral prism into 3D space has a hexagonal prismic envelope. The two octahedral cells project onto the two hexagonal faces. One triangular prismic cell projects onto a triangular prism at the center of the envelope, surrounded by the images of 3 other triangular prismic cells to cover the entire volume of the envelope. The remaining four triangular prismic cells are projected onto the entire volume of the envelope as well, in the same arrangement, except with opposite orientation.