Quasitruncated great stellated dodecahedral prism

Quasitruncated great stellated dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
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	${\sqrt {\frac {39-15{\sqrt {5}}}{8}}}\approx 0.82606$
Hypervolume	$5{\frac {47{\sqrt {5}}-99}{12}}\approx 2.53966$
Dichoral angles	Quit gissid–10/3–stiddip: 90°
	Quit gissid–3–trip: 90°
	Trip–4–stiddip: $\arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18769^{\circ }$
	Stiddip–4–stiddip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Height	1
Central density	13
Number of external pieces	122
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Quit gissiddip
Dual	Great triakis icosahedral tegum
Conjugate	Truncated dodecahedral prism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

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:

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

External links

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

• Klitzing, Richard. "quit gissiddip".