Quasitruncated small stellated dodecahedral prism

Quasitruncated small stellated dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Quit sissiddip
Coxeter diagram	x x5/3x5o ()
Elements
Cells	12 pentagonal prisms, 12 decagrammic prisms, 2 quasitruncated small stellated dodecahedra
Faces	30+60 squares, 24 pentagons, 24 decagrams
Edges	60+60+120
Vertices	120
Vertex figure	Sphenoid, edge lengths (1+√5)/2, √5–√5)/2, √(5–√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {19-5{\sqrt {5}}}{8}}}\approx 0.98867$
Hypervolume	$11{\frac {3{\sqrt {5}}-5}{4}}\approx 4.69756$
Dichoral angles	Stiddip–4–stiddip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Quit sissid–5–pip: 90°
	Quit sissid–10/3–stiddip: 90°
	Stiddip–4–pip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Height	1
Central density	9
Number of external pieces	110
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Quit sissiddip
Dual	Great pentakis dodecahedral tegum
Conjugate	Truncated great dodecahedral prism
Abstract & topological properties
Euler characteristic	–8
Orientable	Yes
Properties
Symmetry	H3×A1</ub>, order 240
Convex	No
Nature	Tame

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

Vertex coordinates

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

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#906).

• Klitzing, Richard. "quit sissiddip".