Truncated faceted hexacosichoron

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Truncated faceted hexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymTiffix
Coxeter diagramo5/2o5x3x ()
Elements
Cells120 great dodecahedra, 120 truncated icosahedra
Faces1440 pentagons, 1200 hexagons
Edges720+3600
Vertices1440
Vertex figurePentagrammic pyramid, edge lengths (1+5)/2 (base) and 3 (side)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGad–5–ti: 144°
 Ti–6–ti: 120°
Central density4
Number of external pieces2520
Level of complexity13
Related polytopes
ArmyTex
RegimentTex
ConjugateTruncated great faceted hexacosichoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count57600
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The truncated faceted hexacosichoron, or tiffix, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 120 truncated icosahedra. One great dodecahedron and five truncated icosahedra join at each vertex. As the name suggests, it can be obtained by truncating the faceted hexacosichoron.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the truncated hexacosichoron.

Cross-sections[edit | edit source]

External links[edit | edit source]