Great dodecicosidodecahedral prism

Great dodecicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gaddiddip
Coxeter diagram	x x5/3x5/2o3*b ()
Elements
Cells	20 triangular prisms, 12 pentagrammic prisms, 12 decagrammic prisms, 2 great dodecicosidodecahedra
Faces	40 triangles, 60+60 squares, 24 pentagrams, 24 decagrams
Edges	60+120+120
Vertices	120
Vertex figure	Isosceles trapezoidal pyramid, edge lengths 1, √(5–√5)/2, (√5–1)/2, √(5–√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403$
Hypervolume	$2\frac{45-17\sqrt5}{3} ≈ 4.6790$
Dichoral angles	Stip–4–stiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Trip–4–stiddip: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232°$
	Gaddid–5/2–stip: 90°
	Gaddid–3–trip: 90°
	Gaddid–10/3–stiddip: 90°
Height	1
Central density	10
Number of pieces	182
Related polytopes
Army	Semi-uniform Tipe
Regiment	Gaddiddip
Dual	Great dodecacronic hexecontahedral tegum
Conjugate	Small dodecicosidodecahedral prism
Abstract properties
Euler characteristic	–18
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The great dodecicosidodecahedral prism or gaddiddip is a prismatic uniform polychoron that consists of 2 great dodecicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 12 decagrammic prisms. Each vertex joins 1 great dodecicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 decagrammic prisms. As the name suggests, it is a prism based on the great dodecicosidodecahedron.

The great dodecicosidodecahedral prism can be vertex-inscribed into the grand ditetrahedronary hexacosidishecatonicosachoron.

Vertex coordinates

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

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

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

• $\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac12\right),$
• $\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{4},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#938).

• Klitzing, Richard. "gaddiddip".