Snub cubic prism

Snub cubic prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sniccup
Coxeter diagram	x2s4s3s ()
Elements
Cells	8+24 triangular prisms, 6 cubes, 2 snub cubes
Faces	16+48 triangles, 12+12+24+24 squares
Edges	24+24+48+48
Vertices	48
Vertex figure	Mirror-symmetric (topologically irregular) pentagonal pyramid, edge lengths 1, 1, 1, 1, √2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	≈ 1.43372
Hypervolume	≈ 7.88948
Dichoral angles	Trip–4–trip: ≈ 153.23459°
	Trip–4–cube: ≈ 142.98343°
	Snic–4–cube: 90°
	Snic–3–trip: 90°
Height	1
Central density	1
Number of pieces	40
Level of complexity	20
Related polytopes
Army	Sniccup
Regiment	Sniccup
Dual	Pentagonal icositetrahedral tegum
Conjugate	Snub cubic prism
Abstract properties
Flag count	1920
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B3+×A1, order 48
Convex	Yes
Nature	Tame
Discovered by	{{{discoverer}}}

The snub cubic prism or sniccup is a prismatic uniform polychoron that consists of 2 snub cubes, 6 cubes, and 8+24 triangular prisms. Each vertex joins 1 snub cube, 1 cube, and 4 triangular prisms. It is a prism based on the snub cube. As such it is also a convex segmentochoron (designated K-4.60 on Richard Klitzing's list).

Gallery

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  Geogebra render

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  Cross-sections

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  Net

Vertex coordinates

The vertices of a snub cubic prism of edge length 1 are given by all even permutations and even sign changes, as well as odd permutations and odd sign changes of the first three coordinates of:

• $\left(c_1,\,c_2,\,c_3,\,±\frac12\right),$

where

• $c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$
• $c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$
• $c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#951).

• Klitzing, Richard. "Sniccup".

• Wikipedia Contributors. "Snub cubic prism".