Pentagonal hexecontahedron

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Pentagonal hexecontahedron
Rank3
TypeUniform dual
Notation
Bowers style acronymSapedit
Coxeter diagramp5p3p ()
Conway notationgD
Elements
Faces60 floret pentagons
Edges30+60+60
Vertices12+20+60
Vertex figure12 pentagons, 20+60 triangles
Measures (edge length 1)
Dihedral angle≈ 153.17873°
Central density1
Number of external pieces60
Level of complexity10
Related polytopes
ArmySapedit
RegimentSapedit
DualSnub dodecahedron
ConjugatesGreat pentagonal hexecontahedron, great inverted pentagonal hexecontahedron, great pentagrammic hexecontahedron
Abstract & topological properties
Flag count600
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH3+, order 60
ConvexYes
NatureTame

The pentagonal hexecontahedron, also called the small petaloid ditriacontahedron, is one of the 13 Catalan solids. It has 60 floret pentagons as faces, with 12 order-5 and 20+60 order-3 vertices. It is the dual of the uniform snub dodecahedron.

Each face of this polyhedron is an irregular pentagon with 3 short and 2 long edges. The long edges are around 1.74985 times the length of the shorter ones. Each face has one angle (between two long edges) measuring around 67.45351°, while its other four angles measure around 118.13662°.

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