Compound of five great dodecahedra

Compound of five great dodecahedra
(OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Presipsi
Elements
Components	5 great dodecahedra
Faces	60 pentagons
Edges	30+120
Vertices	60
Vertex figure	Regular pentagram, edge length (1+√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106$
Inradius	${\sqrt {\frac {5+{\sqrt {5}}}{40}}}\approx 0.42533$
Volume	$5{\frac {5+3{\sqrt {5}}}{4}}\approx 14.63525$
Dihedral angle	$\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Central density	15
Number of external pieces	1740
Level of complexity	103
Related polytopes
Army	Semi-uniform Srid, edge lengths ${\frac {1}{2}}$ (pentagons), ${\frac {{\sqrt {5}}-1}{4}}$ (triangles)
Regiment	Sne
Dual	Compound of five small stellated dodecahedra
Conjugate	Compound of five small stellated dodecahedra
Convex core	Deltoidal hexecontahedron
Abstract & topological properties
Flag count	600
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The pentagonal retrosnub pseudicosicosahedron, presipsi, or compound of five great dodecahedra is a uniform polyhedron compound. It consists of 60 pentagons, with five faces joining at a vertex.

It can be constructed from the snub icosicosahedron by replacing each icosahedron with the great dodecahedron with which it shares its edges.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the snub icosicosahedron.

External links

• Bowers, Jonathan. "Polyhedron Category C4: Ikers" (#26).

• Klitzing, Richard. "presipsi".
• Wikipedia contributors. "Compound of five great dodecahedra".