complementary cell

Bitruncated 5-cell

Schlegel diagram with alternate cells hidden.
Type Uniform polychoron
Uniform index 6
Cells 10 (3.6.6)
Faces 20 {3}
20 {6}
Edges 60
Vertices 30
Vertex figure 4 (3.6.6)
(Tetragonal disphenoid)
Coxeter-Dynkin diagram - Schläfli symbol t1,2{3,3,3}
Symmetry group A4, [3,3,3], order 240
Properties convex cell-transitive

In four dimensional geometry, the bitruncated 5-cell, or bitruncated pentachoron, is a 4-dimensional polytope, or polychoron, composed of 10 cells in the shape of truncated tetrahedra. Each hexagonal face of the truncated tetrahedra is joined in complementary orientation to the neighboring truncated tetrahedron. Each edge is shared by two hexagonal faces and one triangular face.

The bitruncated 5-cell is the intersection of two pentachora in dual configuration.

It is one of the two non-regular uniform polychora which are cell-transitive. The other is the bitruncated 24-cell, which is composed of 48 truncated cubes.

Alternative names

  • Bitruncated pentachoron
  • Bitruncated pentatope
  • Bitruncated 4-simplex
  • (Truncated-tetrahedral) decachoron
  • Deca (Jonathan Bowers: for decachoron)


stereographic projection of spherical polychoron

Net (polytope)

See also

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