Faceted rectified hexateron

Faceted rectified hexateron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Firx
Coxeter diagram	(x3/2o3o3o3x)/2 (/2)
Elements
Tera	6 pentachora, 15 tetrahedral prisms, 10 triangular duoprisms
Cells	30 tetrahedra, 60 triangular prisms
Faces	60 triangles, 45 squares
Edges	60
Vertices	15
Vertex figure	Tetrahedral retroprism, edge lengths 1 (base) and √2 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {6}}{3}}\approx 0.81650$
Diteral angles	Pen–tet–tepe: $\arccos \left({\frac {\sqrt {10}}{5}}\right)\approx 50.76848^{\circ }$
	Tepe–trip–triddip: 45°
Related polytopes
Army	Rix
Regiment	Rix
Conjugate	None
Abstract & topological properties
Flag count	5760
Orientable	No
Properties
Symmetry	A5, order 720
Convex	No
Nature	Tame

The faceted rectified hexateron, or firx, is a nonconvex uniform polyteron. It consists of 6 regular pentachora, 15 tetrahedral prisms, and 10 triangular duoprisms (which pass through the center). 2 pentachora, 8 tetrahedral prisms, and 6 triangular duoprisms join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 3: Rectates" (#27).

• Klitzing, Richard. "firx".