Augmented pentagonal prism

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Augmented pentagonal prism
Rank3
TypeCRF
Notation
Bowers style acronymAupip
Coxeter diagramoxxx oxfo&#xt
Elements
Faces2+2 triangles, 2+2 squares, 2 pentagons
Edges1+2+2+2+4+4+4
Vertices1+2+4+4
Vertex figures1 square, edge length 1
 4 irregular tetragons, edge lengths 1, 1, 2, (1+5)/2
 2+4 isosceles triangles, edge lengths (1+5)/2, 2, 2
Measures (edge length 1)
Volume
Dihedral angles3–4 join:
 3–5 join:
 3–3 pyramidal:
 4–4: 108°
 4–5: 90°
Central density1
Number of external pieces10
Level of complexity19
Related polytopes
ArmyAupip
RegimentAupip
DualLateromonotruncated pentagonal tegum
ConjugatesAugmented pentagrammic prism, Excavated pentagonal prism, Excavated pentagrammic prism
Abstract & topological properties
Flag count76
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
ConvexYes
NatureTame

The augmented pentagonal prism is one of the 92 Johnson solids (J52). It consists of 2+2 triangles, 2 +2squares, and 2 pentagons. It can be constructed by attaching a square pyramid to one of the square faces of the pentagonal prism.

Vertex coordinates[edit | edit source]

An augmented pentagonal prism of edge length 1 has the following vertices:

External links[edit | edit source]