Truncated octahedral prism


Truncated octahedral prism
Truncated octahedral prism
Truncated octahedral prism.png
Schlegel diagram
Type Prismatic uniform polychoron
Uniform index 54
Schläfli symbol t0,1{3,4}×{}
t0,1,2{3,3}×{}
Coxeter-Dynkin CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.png
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.png
Cells 16:
2 Truncated octahedron.png 3.6.6
6 Hexahedron.png {4,3}
8 Hexagonal prism.png {}x{6}
Faces 64:
48 {4}
16 {6}
Edges 96
Vertices 48
Vertex configuration Isosceles-triangular pyramid
Symmetry group [3,4,2], order 96
[3,3,2], order 48
Properties convex

In 4-dimensional geometry, a truncated octahedral prism is a convex uniform polychoron (four dimensional polytope). This polychoron has 16 cells (2 truncated octahedra connected by 6 cubes, 8 hexagonal prisms.) It has 64 faces (48 squares and 16 hexagons), and 96 edges and 48 vertices.

It has two symmetry constructions, one from the truncated octahedron, and one as an omnitruncation of the tetrahedron.

Alternative names:

  1. Truncated-octahedral dyadic prism (Norman W. Johnson)
  2. Truncated octahedral hyperprism
  3. Tope (Jonathan Bowers: for truncated-octahedral prism)

It is one of 18 uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids and Archimedean solids.

External links