Small stellated dodecahedral prism

Small stellated dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sissiddip
Coxeter diagram	x x5/2o5o ()
Elements
Cells	12 pentagrammic prisms, 2 small stellated dodecahedra
Faces	30 squares, 24 pentagrams
Edges	12+60
Vertices	24
Vertex figure	Pentagonal pyramid, edge lengths (√5–1)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7-{\sqrt {5}}}{8}}}\approx 0.77168$
Hypervolume	${\frac {3{\sqrt {5}}-5}{4}}\approx 0.42705$
Dichoral angles	Stip–4–stip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Sissid–5/2–stip: 90°
Height	1
Central density	3
Number of external pieces	62
Related polytopes
Army	Semi-uniform Ipe
Regiment	Sissiddip
Dual	Great dodecahedral tegum
Conjugate	Great dodecahedral prism
Abstract & topological properties
Euler characteristic	–8
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small stellated dodecahedral prism or sissiddip is a prismatic uniform polychoron that consists of 2 small stellated dodecahedra and 12 pentagrammic prisms. Each vertex joins 1 small stellated dodecahedron and 5 pentagrammic prisms. As the name suggests, it is a prism based on the small stellated dodecahedron.

Gallery

• 

  Cross-sections

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  Another projection

Vertex coordinates

The vertices of a small stellated dodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1}{2}}\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#894).

• Klitzing, Richard. "sissiddip".