Tesseractihexadecaquasitruncated tesseractihexadecachoron

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Tesseractihexadecaquasitruncated tesseractihexadecachoron
Rank4
TypeUniform
Notation
Bowers style acronymThaquitoth
Coxeter diagramo3x3x4x4/3*b ()
Elements
Cells16 truncated tetrahedra, 8 quasitruncated hexahedra, 8 cuboctatruncated cuboctahedra
Faces64 triangles, 64 hexagons, 24 octagons, 48 octagrams
Edges96+96+192
Vertices192
Vertex figureSphenoid, edge lengths 1 (1), 3 (2), 2+2 (1), and 2–2 (2)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTut–3–quith: 120°
 Cotco–8/3–quith: 90°
 Cotco–8–cotco: 90°
 Cotco–6–tut: 60°
Number of external pieces392
Level of complexity70
Related polytopes
ArmySemi-uniform Prit, edge lengths (small rhombicuboctahedra), 1 (sides of square prisms)
RegimentThaquitoth
ConjugateTesseractihexadecatruncated tesseractihexadecachoron
Convex coreTesseract
Abstract & topological properties
Flag count4608
Euler characteristic–24
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The tesseractihexadecaquasitruncated tesseractihexadecachoron, or thaquitoth, is a nonconvex uniform polychoron that consists of 16 truncated tetrahedra, 8 quasitruncated hexahedra, and 8 cuboctatruncated cuboctahedra. 1 truncated tetrahedron, 1 quasitruncated hexahedron, and 2 cuboctatruncated cuboctahedra join at each vertex.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a tesseractihexadecaquasitruncated tesseractihexadecachoron of edge length 1 are given by all permutations of:

External links[edit | edit source]