# Quasitruncated tesseract

Quasitruncated tesseract
Rank4
TypeUniform
Notation
Bowers style acronymQuitit
Coxeter diagramx4/3x3o3o ()
Elements
Cells16 tetrahedra, 8 quasitruncated hexahedra
Faces64 triangles, 24 octagrams
Edges32+96
Vertices64
Vertex figureTriangular pyramid, edge lengths 1 (base) and 2–2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5-3{\sqrt {2}}}{2}}}\approx 0.61537}$
Hypervolume${\displaystyle {\frac {72{\sqrt {2}}-101}{6}}\approx 0.13723}$
Dichoral anglesQuith–8/3–quith: 90°
Quith–3–tet: 60°
Central density-1
Number of external pieces120
Level of complexity25
Related polytopes
ArmySidpith, edge length ${\displaystyle {\sqrt {2}}-1}$
RegimentQuitit
ConjugateTruncated tesseract
Abstract & topological properties
Flag count1536
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

The quasitruncated tesseract, or quitit, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra and 8 quasitruncated hexahedra. 1 tetrahedron and three quasitruncated hexahedra join at each vertex. As the name suggests, it can be obtained by quasitruncating the tesseract.

## Vertex coordinates

The vertices of a quasitruncated tesseract of edge length 1 are given by all permutations of:

• ${\displaystyle \left(\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right).}$