Octahedral prism
File:Octahedral prism.png File:Octahedral prism-ortho.png Schlegel diagram and skew orthogonal projection
Type
Prismatic uniform 4-polytope
Uniform index
51
Schläfli symbol t{2,3,4} or {3,4}×{}1,3 {3,3,2} or r{3,3}×{}
Coxeter diagram File:CDel node 1.png File:CDel 2.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 6.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 3.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png
Cells
2 (3.3.3.3 File:Octahedron.png 3.4.4 File:Triangular prism.png
Faces
16 {3} , 12 {4}
Edges
30 (2×12+6)
Vertices
12 (2×6)
Vertex figure File:Tetratetrahedral prism verf.png Square pyramid
Dual polytope Cubic bipyramid
Symmetry [3,4,2], order 96+ ,2], order 12
Properties
convex , Hanner polytope
File:Octahedral prism net.png
In geometry , an octahedral prism is a convex uniform 4-polytope . This 4-polytope has 10 polyhedral cells: 2 octahedra connected by 8 triangular prisms .
Octahedral dyadic prism (Norman W. Johnson )
Ope (Jonathan Bowers, for octahedral prism)
Triangular antiprismatic prism
Triangular antiprismatic hyperprism It is a Hanner polytope with vertex coordinates, permuting first 3 coordinates:
([±1,0,0]; ±1) 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.
Transparent Schlegel diagram Transparent Schlegel diagram 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.
It is the second in an infinite series of uniform antiprismatic prisms .
Convex p -gonal 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
File:CDel node.png File:CDel 4.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 6.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 3.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 8.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 4.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 10.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 5.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 12.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 6.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 14.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 7.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 16.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel 8.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node.png File:CDel 2x.png File:CDel p.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png File:CDel node h.png File:CDel p.png File:CDel node h.png File:CDel 2x.png File:CDel node h.png File:CDel 2.png File:CDel node 1.png
Image
File:Digonal antiprismatic prism.png File:Triangular antiprismatic prism.png File:Square antiprismatic prism.png File:Pentagonal antiprismatic prism.png File:Hexagonal antiprismatic prism.png File:Heptagonal antiprismatic prism.png File:Octagonal antiprismatic prism.png File:15-gonal antiprismatic prism.png
Vertex
File:Tetrahedral prism verf.png File:Tetratetrahedral prism verf.png File:Square antiprismatic prism verf2.png File:Pentagonal antiprismatic prism verf.png File:Hexagonal antiprismatic prism verf.png File:Heptagonal antiprismatic prism verf.png File:Octagonal antiprismatic prism verf.png File:Uniform antiprismatic prism verf.png
Cells
2 s{2,2} {4} {3}×{}
2 s{2,3} {3}×{} {3}×{}
2 s{2,4} {4}×{} {3}×{}
2 s{2,5} {5}×{} {3}×{}
2 s{2,6} {6}×{} {3}×{}
2 s{2,7} {7}×{} {3}×{}
2 s{2,8} {8}×{} {3}×{}
2 s{2,p}p {3}×{}
Net
File:Tetrahedron prism net.png File:Octahedron prism net.png File:4-antiprismatic prism net.png File:5-antiprismatic prism net.png File:6-antiprismatic prism net.png File:7-antiprismatic prism net.png File:8-antiprismatic prism net.png File:15-gonal antiprismatic prism verf.png
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 four-dimensional Hanner polytopes ; the other three are the tesseract , the 16-cell , and the dual of the octahedral prism (a cubical bipyramid ).[ 1]
^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
John H. Conway , Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). Norman Johnson Uniform Polytopes , Manuscript (1991)
