Great dodecahedral prism

Great dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
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	$\sqrt{\frac{7+\sqrt5}{8}} ≈ 1.07448$
Hypervolume	$\frac{5+3\sqrt5}{4} ≈ 2.92705$
Dichoral angles	Gad–5–pip: 90°
	Pip–4–pip: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495^\circ$
Height	1
Central density	3
Number of pieces	62
Related polytopes
Army	Ipe
Regiment	Ipe
Dual	Small stellated dodecahedral tegum
Conjugate	Small stellated dodecahedral prism
Abstract properties
Euler characteristic	–8
Topological properties
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".