Prismatorhombated icositetrachoric prism

Prismatorhombated icositetrachoric prism
File:Prismatorhombated icositetrachoric prism.png
Rank	5
Type	Uniform
Notation
Bowers style acronym	Pricope
Coxeter diagram	x x3x4o3x
Elements
Tera	96 triangular-square duoprisms, 96 square-hexagonal duoprisms, 24 truncated octahedral prisms, 24 small rhombicuboctahedral prisms, 2 prismatorhombated icositetrachora,
Cells	192+192 triangular prisms, 144+288+288 cubes, 192+192 hexagonal prisms, 48 truncated octahedra, 48 small rhombicuboctahedra
Faces	384 triangles, 288+288+576+576+576+576 squares, 384 hexagons
Edges	576+576+1152+1152
Vertices	1152
Vertex figure	Isosceles trapezoidal pyramidal pyramid, edge lengths 1, √2, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {33+12{\sqrt {2}}}}{2}}\approx 3.53449$
Hypervolume	$305+224{\sqrt {2}}\approx 621.78384$
Diteral angles	Shiddip–cube–tisdip: $\arccos \left(-{\frac {2{\sqrt {2}}}{3}}\right)\approx 160.52878^{\circ }$
	Tope–hip–shiddip: 150°
	Sircope–trip–tisdip: 150°
	Sircope–4–shiddip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Sircope–cube–tope: 135°
	Prico–sirco–sircope: 90°
	Prico–toe–tope: 90°
	Prico–hip–shiddip: 90°
	Prico–trip–tisdip: 90°
Height	1
Central density	1
Number of external pieces	242
Level of complexity	80
Related polytopes
Army	Pricope
Regiment	Pricope
Dual	Deltopyramidal pentacosiheptacontahexachoric tegum
Conjugate	Prismatoquasirhombated icositetrachoric prism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	F4×A1, order 2304
Convex	Yes
Nature	Tame

The prismatorhombated icositetrachoric prism or pricope is a prismatic uniform polyteron that consists of 2 prismatorhombated icositetrachora, 24 small rhombicuboctahedral prisms, 24 truncated octahedral prisms, 96 square-hexagonal duoprisms, and 96 triangular-square duoprisms. 1 prismatorhombated icositetrachora, 1 small rhombicuboctahedral prism, 1 truncated octahedral prism, 1 triangular-square duoprism, and 2 square-hexagonal duoprisms join at each vertex. As the name suggests, it is a prism based on the prismatorhombated icositetrachoron, which also makes it a convex segmentoteron.

This polyteron can be subsymmetrically faceted into a prismatorhombisnub icositetrachoric alterprism, although it cannot be made scaliform.

Vertex coordinates

The vertices of a prismatorhombated icositetrachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:

• $\left(\pm {\frac {2+3{\sqrt {2}}}{2}},\,\pm {\sqrt {2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1+3{\sqrt {2}}}{2}},\,\pm {\frac {1+2{\sqrt {2}}}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).$

External links

• Klitzing, Richard. "Pricope".