Retroprismatorhombated hexateron

Retroprismatorhombated hexateron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Rapirx
Coxeter diagram	o3x3x3x3/2o3*c ()
Elements
Tera	20 triangular duoprisms, 6 decachora, 6 great rhombated pentachora, 6 prismatotrispentachora
Cells	60+60 triangular prisms, 30+30 truncated tettrahedra, 15 octahemioctahedra, 30 truncated octahedra
Faces	60+60+60 triangles, 180 squares, 60+120 hexagons
Edges	180+180+180
Vertices	180
Vertex figure	Skewed Bowtie scalene, base edge lengths 1 and √3, opposite edge length 1, lacing lengths √2 and √3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {33}}{3}}\approx 1.91485$
Hypervolume	${\frac {197{\sqrt {3}}}{10}}\approx 34.12140$
Diteral angles	Pittip–trip–triddip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Pittip–tut–deca: $\arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }$
	Pittip–oho–pittip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Deca–tut–grip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Pittip–toe–grip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Grip–trip–triddip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Related polytopes
Army	Pirx
Regiment	Pirx
Conjugate	None
Abstract & topological properties
Flag count	28800
Orientable	Yes
Properties
Symmetry	A5, order 720
Convex	No
Nature	Tame

The retroprismatorhombated hexateron, or rapirx, is a nonconvex uniform polyteron. It consists of 6 prismatotrispentachora, 6 decachora, 6 great rhombated pentachora, and 20 triangular duoprisms. 2 prismatotrispentachora, 1 decachoron, 1 triangular duoprism, and 2 great rhombated pentachora join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#830).

• Klitzing, Richard. "rapirx".