- Octahedral prism
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Octahedral prism 
Schlegel diagramType 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 12Properties convex 
Transparent Schlegel diagram
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
Related polytopes
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.
Alternative names
- Octahedral dyadic prism (Norman W. Johnson)
- Ope (Jonathan Bowers, for octahedral prism)
- Triangular antiprismatic prism
- Triangular antiprismatic hyperprism
Structure
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.
Projections
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.
External links
- 6. Convex uniform prismatic polychora - Model 51, George Olshevsky.
- Richard Klitzing, 4D uniform polytopes (polychora), x x3o4o - ope
Categories:- Four-dimensional geometry
- Polychora
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