Compound of five small stellated dodecahedra

Compound of five small stellated dodecahedra
(OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Passipsi
Elements
Components	5 small stellated dodecahedra
Faces	60 pentagrams
Edges	30+120
Vertices	60
Vertex figure	Regular pentagon, edge length (√5–1)/2
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5-{\sqrt {5}}}{8}}}\approx 0.58779$
Inradius	${\sqrt {\frac {5-{\sqrt {5}}}{40}}}\approx 0.26287$
Volume	$5{\frac {3{\sqrt {5}}-5}{4}}\approx 2.13525$
Dihedral angle	$\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
Central density	15
Number of external pieces	300
Level of complexity	18
Related polytopes
Army	Semi-uniform Srid, edge lengths ${\frac {{\sqrt {5}}-1}{4}}$ (pentagons), ${\frac {3-{\sqrt {5}}}{4}}$ (triangles)
Regiment	Passipsi
Dual	Compound of five great dodecahedra
Conjugate	Compound of five great dodecahedra
Convex core	Deltoidal hexecontahedron
Abstract & topological properties
Flag count	600
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The pentagrammatic snub pseudicosicosahedron, passipsi, or compound of five small stellated dodecahedra is a uniform polyhedron compound. It consists of 60 pentagrams, with five faces joining at a vertex.

Gallery

Vertex coordinates

The vertices of a pentagrammatic snub pseudicosicosahedron of edge length 1 can be given by all even permutations of:

• $\left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{4}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {5}}}{8}},\,\pm {\frac {1}{4}},\,\pm {\frac {5-{\sqrt {5}}}{8}}\right)$,
• $\left(\pm {\frac {{\sqrt {5}}-1}{8}},\,\pm {\frac {3-{\sqrt {5}}}{8}},\,\pm {\frac {\sqrt {5}}{4}}\right)$.

External links

• Bowers, Jonathan. "Polyhedron Category C4: Ikers" (#27).

• Klitzing, Richard. "passipsi".
• Wikipedia contributors. "Compound of five small stellated dodecahedra".