Quasitruncated tesseract

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.

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
Hypervolume
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
RegimentQuitit
ConjugateTruncated tesseract
Convex coreHexadecachoron
Abstract & topological properties
Flag count1536
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexNo
NatureTame

Vertex coordinates edit

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

  •  

Cross-sections edit

External links edit