Octahedral prism  

Schlegel diagram and skew orthogonal projection  
Type  Prismatic uniform 4polytope 
Uniform index  51 
Schläfli symbol  t{2,3,4} or {3,4}×{} t_{1,3}{3,3,2} or r{3,3}×{} s{2,6}×{} sr{3,2}×{} 
Coxeter diagram  
Cells  2 (3.3.3.3) 8 (3.4.4) 
Faces  16 {3}, 12 {4} 
Edges  30 (2×12+6) 
Vertices  12 (2×6) 
Vertex figure  Square pyramid 
Dual polytope  Cubic bipyramid 
Symmetry  [3,4,2], order 96 [3,3,2], order 48 [6,2+,2], order 24 [(3,2)^{+},2], order 12 
Properties  convex, Hanner polytope 
Net 
In geometry, an octahedral prism is a convex uniform 4polytope. This 4polytope has 10 polyhedral cells: 2 octahedra connected by 8 triangular prisms.
It is a Hanner polytope with vertex coordinates, permuting first 3 coordinates:
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 octahedronfirst 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 triangularprismfirst 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.
It is the second in an infinite series of uniform antiprismatic prisms.
Name  s{2,2}×{}  s{2,3}×{}  s{2,4}×{}  s{2,5}×{}  s{2,6}×{}  s{2,7}×{}  s{2,8}×{}  s{2,p}×{} 

Coxeter diagram 








Image  
Vertex figure 

Cells  2 s{2,2} (2) {2}×{}={4} 4 {3}×{} 
2 s{2,3} 2 {3}×{} 6 {3}×{} 
2 s{2,4} 2 {4}×{} 8 {3}×{} 
2 s{2,5} 2 {5}×{} 10 {3}×{} 
2 s{2,6} 2 {6}×{} 12 {3}×{} 
2 s{2,7} 2 {7}×{} 14 {3}×{} 
2 s{2,8} 2 {8}×{} 16 {3}×{} 
2 s{2,p} 2 {p}×{} 2p {3}×{} 
Net 
It is one of 18 uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids and Archimedean solids.
It is one of four fourdimensional Hanner polytopes; the other three are the tesseract, the 16cell, and the dual of the octahedral prism (a cubical bipyramid).^{[1]}