Great ditrigonal dodecicosidodecahedral prism

Great ditrigonal dodecicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidditdiddip
Coxeter diagram	x x5/3x3o5*b ()
Elements
Cells	20 triangular prisms, 12 pentagonal prisms, 12 decagrammic prisms, 2 great ditrigonal dodecicosidodecahedra
Faces	40 triangles, 60+60 squares, 24 pentagons, 24 decagrams
Edges	60+120+120
Vertices	120
Vertex figure	Isosceles trapezoidal pyramid, edge lengths 1, √(5–√5)/2, (1+√5)/2, √(5–√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{19-3\sqrt5}{8}} ≈ 1.23955$
Hypervolume	$7\frac{15-\sqrt5}{2} ≈ 14.89125$
Dichoral angles	Trip–4–stiddip: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263^\circ$
	Pip–4–stiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ$
	Gidditdid–5–pip: 90°
	Gidditdid–3–trip: 90°
	Gidditdid–10/3–stiddip: 90°
Height	1
Central density	4
Number of pieces	154
Related polytopes
Army	Semi-uniform Tiddip
Regiment	Gidditdiddip
Dual	Great ditrigonal dodecacronic hexecontahedral tegum
Conjugate	Small ditrigonal dodecicosidodecahedral prism
Abstract properties
Euler characteristic	–18
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

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

Vertex coordinates

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

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#935).

• Klitzing, Richard. "gidditdiddip".