Quasitruncated small stellated dodecahedral prism

Quasitruncated small stellated dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
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	$\sqrt{\frac{19-5\sqrt5}{8}} ≈ 0.98867$
Hypervolume	$11\frac{3\sqrt5-5}{4} ≈ 4.69756$
Dichoral angles	Stiddip–4–stiddip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	Quit sissid–5–pip: 90°
	Quit sissid–10/3–stiddip: 90°
	Stiddip–4–pip: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495°$
Height	1
Central density	9
Number of pieces	110
Related polytopes
Army	Semi-uniform Sriddip
Regiment	Quit sissiddip
Dual	Great pentakis dodecahedral tegum
Conjugate	Truncated great dodecahedral prism
Abstract properties
Euler characteristic	–8
Topological properties
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:

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

External links

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

• Klitzing, Richard. "quit sissiddip".