Pentagonal-snub cubic duoprism

Pentagonal-snub cubic duoprism
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Pesnic
Coxeter diagram	x5o s4s3s
Elements
Tera	8+24 triangular-pentagonal duoprisms, 6 square-pentagonal duoprisms, 5 snub cubic prisms
Cells	40+120 triangular prisms, 30 cubes, 12+24+24 pentagonal prisms, 5 snub cubes
Faces	40+120 triangles, 30+60+120+120 squares, 24 pentagons
Edges	60+120+120+120
Vertices	120
Vertex figure	Mirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, √2 (base pentagon), (1+√5)/2 (top edge), √2 (side edges)
Measures (edge length 1)
Circumradius	≈ 1.59034
Hypervolume	≈ 13.57367
Diteral angles	Trapedip–pip–trapedip: ≈ 153.23459°
	Trapedip–pip–squipdip: ≈ 142.98343°
	Sniccup–snic–sniccup: 108°
	Trapedip–trip–sniccup: 90°
	Squipdip–cube–sniccup: 90°
Central density	1
Number of external pieces	43
Level of complexity	50
Related polytopes
Army	Pesnic
Regiment	Pesnic
Dual	Pentagonal-pentagonal icositetrahedral duotegum
Conjugate	Pentagrammic-snub cubic duoprism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B3+×H2, order 240
Convex	Yes
Nature	Tame

The pentagonal-snub cubic duoprism or pesnic is a convex uniform duoprism that consists of 5 snub cubic prisms, 6 square-pentagonal duoprisms, and 32 triangular-pentagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-pentagonal duoprisms, and 1 square-pentagonal duoprism.

Vertex coordinates

The vertices of a pentagonal-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of:

• $\left(0,\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}},\,c_{1},\,c_{2},\,c_{3}\right),$
• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5-{\sqrt {5}}}{40}}},\,c_{1},\,c_{2},\,c_{3}\right),$
• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{20}}},\,c_{1},\,c_{2},\,c_{3}\right),$

where

• $c_{1}={\sqrt {{\frac {1}{12}}\left(4-{\sqrt[{3}]{17+3{\sqrt {33}}}}-{\sqrt[{3}]{17-3{\sqrt {33}}}}\right)}},$
• $c_{2}={\sqrt {{\frac {1}{12}}\left(2+{\sqrt[{3}]{17+3{\sqrt {33}}}}+{\sqrt[{3}]{17-3{\sqrt {33}}}}\right)}},$
• $c_{3}={\sqrt {{\frac {1}{12}}\left(4+{\sqrt[{3}]{199+3{\sqrt {33}}}}+{\sqrt[{3}]{199-3{\sqrt {33}}}}\right)}}.$