Retroprismatorhombated triacontaditeron

Retroprismatorhombated triacontaditeron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Repirt
Coxeter diagram	o4x3x3x3/2o3*c ()
Elements
Tera	80 triangular-square duoprisms, 32 prismatotrispentachora, 10 tesseractihexadecachora, 10 truncated icositetrachora
Cells	320 triangular prisms, 240 cubes, 160 truncated tetrahedra, 80 octahemioctahedra, 80+160 truncated octahedra
Faces	320+320 triangles, 240+960 squares, 320+640 hexagons
Edges	960+960+960
Vertices	960
Vertex figure	Skewed bowtie scalene, base edge lengths 1 and √3, opposite edge length √2, lacing lengths √2 and √3
Measures (edge length 1)
Circumradius	3
Hypervolume	${\frac {17917{\sqrt {2}}}{30}}\approx 844.61548$
Diteral angles	Pittip–trip–tisdip: $\arccos \left(-{\frac {\sqrt {15}}{5}}\right)\approx 140.76848^{\circ }$
	Pittip–oho–pittip: $\arccos \left(-{\frac {3}{5}}\right)\approx 126.86990^{\circ }$
	Tah–tut–pittip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Tah–toe–tico: 90°
	Tico–toe–pittip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
	Tico–cube–tisdip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Related polytopes
Army	Pirt
Regiment	Pirt
Conjugate	None
Abstract & topological properties
Flag count	153600
Orientable	Yes
Properties
Symmetry	B5, order 3840
Convex	No
Nature	Tame

The retroprismatorhombated triacontaditeron, or repirt, is a uniform polyteron. It consists of 10 tesseractihexadecachora, 32 prismatotrispentachora, 10 truncated icositetrachora, and 80 triangular-square duoprisms. 2 prismatotrispentachora, 1 tesseractihexadecachoron, 1 triangular-square duoprism, and 2 truncated icositetrachora join at each vertex.

Vertex coordinates

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

Representations

A retroprismatorhombated triacontaditeron has the following Coxeter diagrams:

• o4x3x3x3/2o3*c (full symmetry)
• x3x3x3/2o3*b3x (D5 symmetry)

External links

• Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#836).

• Klitzing, Richard. "repirt".