Quasitruncated tesseract

Quasitruncated tesseract
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quitit
Coxeter diagram	x4/3x3o3o ()
Elements
Cells	16 tetrahedra, 8 quasitruncated hexahedra
Faces	64 triangles, 24 octagrams
Edges	32+96
Vertices	64
Vertex figure	Triangular 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 angles	Quith–8/3–quith: 90°
	Quith–3–tet: 60°
Central density	-1
Number of external pieces	120
Level of complexity	25
Related polytopes
Army	Sidpith
Regiment	Quitit
Conjugate	Truncated tesseract
Convex core	Hexadecachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

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:

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

Cross-sections

• 
• 

External links

• Bowers, Jonathan. "Category 2: Truncates" (#34).

• Klitzing, Richard. "quitit".