Great stellated dodecahedral prism

The great stellated dodecahedral prism or gissiddip is a prismatic uniform polychoron that consists of 2 great stellated dodecahedra and 12 pentagrammic prisms. Each vertex joins 1 great stellated dodecahedron and 3 pentagrammic prisms. As the name suggests, it is a prism based on the great stellated dodecahedron.

Great stellated dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gissiddip
Coxeter diagram	x x5/2o3o ()
Elements
Cells	12 pentagrammic prisms, 2 great stellated dodecahedra
Faces	30 squares, 24 pentagrams
Edges	20+60
Vertices	40
Vertex figure	Triangular pyramid, edge lengths (√5–1)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {11-3{\sqrt {5}}}{8}}}\approx 0.73244$
Hypervolume	${\frac {7{\sqrt {5}}-15}{4}}\approx 0.16312$
Dichoral angles	Gissid–5/2–stip: 90°
	Stip–4–stip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Height	1
Central density	7
Number of external pieces	62
Related polytopes
Army	Semi-uniform Dope
Regiment	Gissiddip
Dual	Great icosahedral tegum
Conjugate	Dodecahedral prism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

Cross-sections

Vertex coordinates

The vertices of a great stellated dodecahedral prism of edge length 1 are given by:

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

along with all even permutations of:

• $\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {1}{2}}\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#896).

• Klitzing, Richard. "gissiddip".