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Cantellated 5-cell

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Jan 12, 2022

In four-dimensional geometry, a cantellated 5-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation, up to edge-planing) of the regular 5-cell.


5-cell

Cantellated 5-cell

Cantitruncated 5-cell
Orthogonal projections in A4Coxeter plane

There are 2 unique degrees of runcinations of the 5-cell including with permutations truncations.

. . . Cantellated 5-cell . . .

Cantellated 5-cell

Schlegel diagram with
octahedral cells shown
Type Uniform 4-polytope
Schläfli symbol t0,2{3,3,3}
rr{3,3,3}
Coxeter diagram
Cells 20 5 (3.4.3.4)
5 (3.3.3.3)
10 (3.4.4)
Faces 80 50{3}
30{4}
Edges 90
Vertices 30
Vertex figure
Square wedge
Symmetry group A4, [3,3,3], order 120
Properties convex, isogonal
Uniform index 3 4 5
Net

The cantellated5-cell or small rhombated pentachoron is a uniform 4-polytope. It has 30 vertices, 90 edges, 80 faces, and 20 cells. The cells are 5 cuboctahedra, 5 octahedra, and 10 triangular prisms. Each vertex is surrounded by 2 cuboctahedra, 2 triangular prisms, and 1 octahedron; the vertex figure is a nonuniform triangular prism.

. . . Cantellated 5-cell . . .

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. . . Cantellated 5-cell . . .