Great dodecicosidodecahedral prism

Great dodecicosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
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	${\frac {{\sqrt {10}}-{\sqrt {2}}}{2}}\approx 0.87403$
Hypervolume	$2{\frac {45-17{\sqrt {5}}}{3}}\approx 4.6790$
Dichoral angles	Stip–4–stiddip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Trip–4–stiddip: $\arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }$
	Gaddid–5/2–stip: 90°
	Gaddid–3–trip: 90°
	Gaddid–10/3–stiddip: 90°
Height	1
Central density	10
Number of external pieces	182
Related polytopes
Army	Semi-uniform Tipe
Regiment	Gaddiddip
Dual	Great dodecacronic hexecontahedral tegum
Conjugate	Small dodecicosidodecahedral prism
Abstract & topological properties
Euler characteristic	–18
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:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {1}{2}}\right),$

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

• $\left(0,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right).$

External links

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

• Klitzing, Richard. "gaddiddip".