Faceted rectified tesseract

Faceted rectified tesseract
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Firt
Coxeter diagram	x3x3o3o3/2*a ()
Elements
Cells	16 tetrahedra 16 truncated tetrahedra
Faces	64 triangles, 32 hexagons
Edges	96
Vertices	32
Vertex figure	Triangular retroprism, edge lengths 1 (base) and √3 (sides)
Edge figure	tet 3 tut 6 tut 6 tut 3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {6}}{2}}\approx 1.22475$
Hypervolume	${\frac {10}{3}}\approx 3.33333$
Dichoral angle	Tet–3–tut: 60° Tut–6–tut: 60°
Central density	4
Number of external pieces	368
Level of complexity	23
Related polytopes
Army	Rit
Regiment	Rit
Conjugate	None
Convex core	Hexadecachoron
Abstract & topological properties
Flag count	1536
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Flag orbits	4
Convex	No
Nature	Tame

The faceted rectified tesseract, or firt, is a nonconvex uniform polychoron that consists of 16 regular tetrahedra and 16 truncated tetrahedra. Two tetrahedra and six truncated tetrahedra join at each vertex.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified tesseract.

External links

• Bowers, Jonathan. "Category 3: Triangular Rectates" (#43).

• Klitzing, Richard. "firt".