Quasitruncated dodecadodecahedral prism

Quasitruncated dodecadodecahedral prism
	(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quitdiddip
Coxeter diagram	x x5/3x5x ()
Elements
Cells	30 cubes, 12 decagonal prisms, 12 decagrammic prisms, 2 quasitruncated dodecadodecahedra
Faces	60+60+60+60 squares, 24 decagons, 24 decagrams
Edges	120+120+120+120
Vertices	240
Vertex figure	Irregular tetrahedron, edge lengths √2, √(5+√5)/2, √(5–√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume	15
Dichoral angles	Cube–4–stiddip:
	Quitdid–10/3–stiddip: 90°
	Quitdid–10–dip: 90°
	Quitdid–4–cube: 90°
	Dip–4–stiddip:
	Cube–4–dip:
Height	1
Central density	-3
Number of pieces	406
Related polytopes
Army	Semi-uniform Griddip
Regiment	Quitdiddip
Dual	Medial disdyakis triacontahedral tegum
Conjugate	Quasitruncated dodecadodecahedral prism
Abstract properties
Euler characteristic	–8
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The quasitruncated dodecadodecahedral prism or quitdiddip, is a prismatic uniform polychoron that consists of 2 quasitruncated dodecadodecahedra, 12 decagrammic prisms, 12 decagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. as the name suggests, it is a prism based on the quasitruncated dodecadodecahedron.

The great rhombicosidodecahedral pirsm can be vertex-inscribed into the rectified small ditrigonary hexacosihecatonicosachoron.

Vertex coordinates[edit | edit source]

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

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

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