Quasitruncated small stellated dodecahedron

Quasitruncated small stellated dodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Quit sissid
Coxeter diagram	x5/3x5o ()
Elements
Faces	12 pentagons, 12 decagrams
Edges	30+60
Vertices	60
Vertex figure	Isosceles triangle, edge lengths (1+√5)/2, √(5–√5)/2, √(5–√5)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{17-5\sqrt5}{8}} ≈ 0.85291$
Volume	$11\frac{3\sqrt5-5}{4} ≈ 4.69756$
Dihedral angles	10/3–10/3: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
	5–10/3: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495°$
Central density	9
Number of pieces	132
Level of complexity	11
Related polytopes
Army	Srid
Regiment	Quit sissid
Dual	Great pentakis dodecahedron
Conjugate	Truncated great dodecahedron
Convex core	Dodecahedron
Abstract properties
Euler characteristic	–6
Topological properties
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The quasitruncated small stellated dodecahedron, or quit sissid, also called the small stellated truncated dodecahedron, is a uniform polyhedron. It consists of 12 pentagons and 12 decagrams. Each vertex joins one pentagon and two decagrams. As the name suggests, it can be obtained by the quasitruncation of the small stellated dodecahedron.

Vertex coordinates

A quasitruncated small stellated dodecahedron of edge length 1 has vertex coordinates given by all permutations of:

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

together with all even permutations of:

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

Related polyhedra

o5/3o5o truncations

Name	OBSA	Schläfli symbol	CD diagram	Picture
Small stellated dodecahedron	sissid	{5/3,5}	x5/3o5o ()
Quasitruncated small stellated dodecahedron	quit sissid	t{5/3,5}	x5/3x5o ()
Dodecadodecahedron	did	r{5,5/3}	o5/3x5o ()
Truncated great dodecahedron	tigid	t{5,5/3}	o5/3x5x ()
Great dodecahedron	gad	{5,5/3}	o5/3o5x ()
Complex ditrigonal rhombidodecadodecahedron (degenerate, ditdid+rhom)	cadditradid	rr{5,5/3}	x5/3o5x ()
Quasitruncated dodecadodecahedron	quitdid	tr{5,5/3}	x5/3x5x ()
Inverted snub dodecadodecahedron	isdid	sr{5,5/3}	s5/3s5s ()

External links

• Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#18).

• Klitzing, Richard. "Quit sissid".

• Wikipedia Contributors. "Small stellated truncated dodecahedron".
• McCooey, David. "Small Stellated Truncated Dodecahedron"