Rhombidodecadodecahedral prism

Rhombidodecadodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Radiddip
Coxeter diagram	x x5/2o5x ()
Elements
Cells	30 cubes, 12 pentagonal prisms, 12 pentagrammic prisms, 2 rhombidodecadodecahedra
Faces	60+60+60 squares, 24 pentagons, 24 pentagrams
Edges	60+120+120
Vertices	120
Vertex figure	Isosceles trapezoidal pyramid, edge lengths (√5–1)/2, √2, (1+√5)/2, √2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt2 ≈ 1.41421$
Hypervolume	$19\sqrt5 ≈ 42.48529$
Dichoral angles	Cube–4–stip: $\arccos\left(-\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 148.28253°$
	Cube–4–pip: $\arccos\left(-\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 121.71747°$
	Raded–5/2–stip: 90°
	Raded–5–pip: 90°
	Raded–4–cube: 90°
Height	1
Central density	3
Related polytopes
Army	Semi-uniform Tipe
Regiment	Radiddip
Dual	Medial deltoidal hexecontahedral tegum
Conjugate	Rhombidodecadodecahedral prism
Abstract & topological properties
Euler characteristic	–8
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The rhombidodecadodecahedral prism or radiddip is a prismatic uniform polychoron that consists of 2 rhombidodecadodecahedra, 12 pentagonal prisms, 12 pentagrammic prisms, and 30 cubes. Each vertex joins 1 rhombidodecadodecahedron, 1 pentagonal prism, 1 pentagrammic prism, and 2 cubes. As the name suggests, it is a prism based on the rhombidodecadodecahedron.

The rhombidodecadodecahedral prism can be vertex-inscribed into the ditetrahedronary dishecatonicosachoron.

Vertex coordinates

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

• $\left(±\frac{\sqrt5}{2},\,±\frac12,\,±\frac12,\,±\frac12\right)$

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

• $\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac12\right),$
• $\left(±1,\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#929).

• Klitzing, Richard. "radiddip".