Dodecadodecahedral prism

Dodecadodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Diddip
Coxeter diagram	x o5/2x5o ()
Elements
Cells	12 pentagonal prisms, 12 pentagrammic prisms, 2 dodecadodecahedra
Faces	60 squares, 24 pentagons, 24 pentagrams
Edges	30+120
Vertices	60
Vertex figure	Rectangular pyramid, edge lengths (1+√5)/2, (√5–1)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt5}{2} ≈ 1.11803$
Hypervolume	5
Dichoral angles	Pip–4–stip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ$
	Did–5–pip: 90°
	Did–5/2–stip: 90°
Height	1
Central density	3
Number of pieces	74
Related polytopes
Army	Semi-uniform Iddip
Regiment	Diddip
Dual	Medial rhombic triacontahedral tegum
Conjugate	dodecadodecahedral prism
Abstract properties
Euler characteristic	–8
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The dodecadodecahedral prism or diddip, is a prismatic uniform polychoron that consists of 2 dodecadodecahedra, 12 pentagrammic prisms, and 12 pentagonal prisms. Each vertex joins 1 dodecadodecahedron, 2 pentagrammic prisms, and 2 pentagonal prisms. As the name suggests, it is a prism based on the dodecadodecahedron.

Cross-sections

Vertex coordinates

The vertices of a dodecadodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

• $\left(±1,\,0,\,0,\,±\frac12\right),$

along with all even permutations of the first three coordinates of:

• $\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#914).

• Klitzing, Richard. "diddip".