# Quasitruncated tesseract

Quasitruncated tesseract Rank4
TypeUniform
SpaceSpherical
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$\sqrt{\frac{5-3\sqrt2}{2}} \approx 0.61537$ Hypervolume$\frac{72\sqrt2-101}{6} \approx 0.13723$ Dichoral anglesQuith–8/3–quith: 90°
Quith–3–tet: 60°
Central density-1
Number of external pieces120
Level of complexity25
Related polytopes
ArmySidpith
RegimentQuitit
ConjugateTruncated tesseract
Abstract & topological properties
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:

• $\left(±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$ 