Retrosphenary hexateron

Retrosphenary hexateron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Rawx
Coxeter diagram	o3o3x3x3/2o3*c ()
Elements
Tera	6 rectified pentachora, 6 truncated pentachora, 6 retrosphenoverted trispentachora
Cells	30 tetrahedra, 30 octahedra, 30 truncated tetrahedra, 15 octahemioctahedra
Faces	20+60+120 triangles, 60 hexagons
Edges	60+180
Vertices	60
Vertex figure	Crossed triangular pyramidal prism, edge lengths 1 (base triangular prism and top edge) and √3 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {15}}{3}}\approx 1.29099$
Hypervolume	${\frac {107{\sqrt {3}}}{120}}\approx 1.54441$
Diteral angles	Rawvtip–oct–rap: $\arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }$
	Rawvtip–oho–rawvtip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Rap–tet–tip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Rawvtip–tut–tip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
Related polytopes
Army	Sarx
Regiment	Sarx
Conjugate	None
Abstract & topological properties
Flag count	11520
Orientable	Yes
Properties
Symmetry	A5, order 720
Convex	No
Nature	Tame

The retrosphenary hexateron, or rawx, is a nonconvex uniform polyteron. It consists of 6 retrosphenoverted trispentachora, 6 rectified pentachora, and 6 truncated pentachora. One rectified pentachoron, 2 truncated pentachora, and 3 retrosphenoverted trispentachora join at each vertex.

Vertex coordinates

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

External links

• Klitzing, Richard. "rawx".