Great dodecahedral prism

Great dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gaddip
Coxeter diagram	x o5/2o5x ()
Elements
Cells	12 pentagonal prisms, 2 great dodecahedra
Faces	30 squares, 24 pentagons
Edges	12+60
Vertices	24
Vertex figure	Pentagrammic pyramid, edge lengths (1+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {7+{\sqrt {5}}}{8}}}\approx 1.07448$
Hypervolume	${\frac {5+3{\sqrt {5}}}{4}}\approx 2.92705$
Dichoral angles	Gad–5–pip: 90°
	Pip–4–pip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Height	1
Central density	3
Number of external pieces	62
Related polytopes
Army	Ipe
Regiment	Ipe
Dual	Small stellated dodecahedral tegum
Conjugate	Small stellated dodecahedral prism
Abstract & topological properties
Euler characteristic	–8
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

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

Gallery

• 

  GeoGebra render

• 

  Card with vertex figure, cell counts, and cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the icosahedral prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#893).

• Klitzing, Richard. "gaddip".