Pentagonal icositetrahedron

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Pentagonal icositetrahedron
Rank3
TypeUniform dual
Notation
Bowers style acronymPedid
Coxeter diagramp4p3p ()
Conway notationgC
Elements
Faces24 floret pentagons
Edges12+24+24
Vertices6+8+24
Vertex figure6 squares, 8+24 triangles
Measures (edge length 1)
Dihedral angle≈ 136.30923°
Central density1
Number of external pieces24
Level of complexity10
Related polytopes
ArmyPedid
RegimentPedid
DualSnub cube
ConjugatePentagonal icositetrahedron
Abstract & topological properties
Flag count240
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB3+, order 24
ConvexYes
NatureTame

The pentagonal icositetrahedron, also called the petaloid disdodecahedron, is one of the 13 Catalan solids. It has 24 floret pentagons as faces, with 6 order-4 and 8+24 order-3 vertices. It is the dual of the uniform snub cube.

Each face of this polyhedron is an irregular pentagon with 3 short and 2 long edges. The long edges are around 1.41964 times the length of the shorter ones. Each face has one angle (between two long edges) measuring around 80.75170°, while its other four angles measure around 114.81207°.

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