Lepidoprismatorhombated hexateron

Lepidoprismatorhombated hexateron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Lapirx
Elements
Tera	15 truncated tetrahedral prisms, 6 great rhombated pentachora, 6 rhombiprismic dispentachora
Cells	60 triangular prisms, 60 hexagonal prisms, 30 truncated tetrahedra, 15 cubohemioctahedra, 30 truncated octahedra
Faces	60 triangles, 90+180 squares, 60+120 hexagons
Edges	180+180+180
Vertices	180
Vertex figure	Skewed bowtie scalene, base edge lengths √2 and √3, opposite edge length 1, lacing lengths √2 and √3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {33}}{3}}\approx 1.91485$
Diteral angles	Ripdip–hip–tuttip: $\arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }$
	Ripdip–cho–ripdip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Ripdip–toe–grip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Grip–trip–tuttip: $\arccos \left({\frac {\sqrt {10}}{10}}\right)\approx 71.56505^{\circ }$
	Grip–tut–tuttip: $\arccos \left({\frac {\sqrt {10}}{5}}\right)\approx 50.76848^{\circ }$
Related polytopes
Army	Pirx
Regiment	Pirx
Conjugate	None
Abstract & topological properties
Flag count	28800
Orientable	No
Properties
Symmetry	A5, order 720
Convex	No
Nature	Tame

The lepidoprismatorhombated hexateron, or lapirx, is a nonconvex uniform polyteron. It consists of 6 rhombiprismic dispentachora, 6 great rhombated pentachora, and 15 truncated tetrahedral prisms. 2 rhombiprismic dispentachora, 2 great rhombated pentachora, and 2 truncated tetrahedral prisms 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" (#831).