Great quasitruncated icosidodecahedral prism

Great quasitruncated icosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gaquatiddip
Coxeter diagram	x x5/3x3x ()
Elements
Cells	30 cubes, 20 hexagonal prisms, 12 decagrammic prisms, 2 great quasitruncated icosidodecahedra
Faces	60+60+60+60 squares, 40 hexagons, 24 decagrams
Edges	120+120+120+120
Vertices	240
Vertex figure	Irregular tetrahedron, edge lengths √2, √3, √(5–√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{8-3\sqrt5} ≈ 1.13657$
Hypervolume	$5(10\sqrt5-19) ≈ 16.80340$
Dichoral angles	Cube–4–stiddip: $\arccos\left(-\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 121.71747°$
	Gaquatid–10/3–stiddip: 90°
	Gaquatid–6–hip: 90°
	Gaquatid–4–cube: 90°
	Hip–4–stiddip: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768°$
	Cube–4–hip: $\arccos\left(\frac{\sqrt{15}-\sqrt3}{6}\right) ≈ 69.09484°$
Height	1
Central density	13
Number of pieces	1142
Related polytopes
Army	Semi-uniform Griddip
Regiment	Gaquatiddip
Dual	Great disdyakis triacontahedral tegum
Conjugate	Great rhombicosidodecahedral prism
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The great quasitruncated icosidodecahedral prism or gaquatiddip, is a prismatic uniform polychoron that consists of 2 great quasitruncated icosidodecahedra, 12 decagrammic prisms, 20 hexagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the great quasitruncated icosidodecahedron.

The great rhombicosidodecahedral pirsm can be vertex-inscribed into the great tritrigonary hexacositrishecatonicosachoron.

Vertex coordinates

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

• $\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2},\,±\frac12\right),$

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

• $\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2},\,±\frac12\right),$
• $\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4},\,±\frac12\right),$
• $\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2},\,±\frac12\right),$
• $\left(±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#948).

• Klitzing, Richard. "gaquatiddip".