Quasitruncated great stellated dodecahedral prism

Quasitruncated great stellated dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quit gissiddip
Coxeter diagram	x x5/3x3o ()
Elements
Cells	20 triangular prisms, 12 decagrammic prisms, 2 quasitruncated great stellated dodecahedra
Faces	40 triangles, 30+60 squares, 24 decagrams
Edges	60+60+120
Vertices	120
Vertex figure	Sphenoid, edge lengths 1, √10–2√5/2, √10–2√5/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{39-15\sqrt5}{8}} ≈ 0.82606$
Hypervolume	$5\frac{47\sqrt5-99}{12} ≈ 2.53966$
Dichoral angles	Quit gissid–10/3–stiddip: 90°
	Quit gissid–3–trip: 90°
	Trip–4–stiddip: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18769°$
	Stiddip–4–stiddip: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495°$
Height	1
Central density	13
Number of pieces	122
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Quit gissiddip
Dual	Great triakis icosahedral tegum
Conjugate	Truncated dodecahedral prism
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame
Discovered by	{{{discoverer}}}

The quasitruncated great stellated dodecahedral prism or quit gissiddip is a prismatic uniform polychoron that consists of 2 quasitruncated great stellated dodecahedra, 12 decagrammic prisms, and 20 triangular prisms. Each vertex joins 1 quasitruncated great stellated dodecahedron, 1 triangular prism, and 2 decagrammic prisms. As the name suggests, it is a prism based on the quasitruncated great stellated dodecahedron.

Vertex coordinates

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

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#907).

• Klitzing, Richard. "quit gissiddip".