Elongated pentagonal orthobirotunda

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Elongated pentagonal orthobirotunda
Rank3
TypeCRF
Notation
Bowers style acronymEpobro
Coxeter diagramxoxxox5ofxxfo&#xt
Stewart notationR5P10R5
J42
Elements
Faces10+10 triangles, 5+5 squares, 2+10 pentagons
Edges10+10+10+10+20+20
Vertices10+10+20
Vertex figures20 rectangles, edge lengths 1 and (1+5)/2
 20 irregular tetragons, edge lengths 1, (1+5)/2, 2, 2
Measures (edge length 1)
Volume
Dihedral angles3–4:
 5–4:
 4–4: 144°
 3–5:
Central density1
Number of external pieces42
Level of complexity16
Related polytopes
ArmyEpobro
RegimentEpobro
DualPentarhombideltorthodecatetragonal tetracontahedron
ConjugateElongated pentagrammic orthobirotunda
Abstract & topological properties
Flag count320
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×A1, order 20
ConvexYes
NatureTame

The elongated pentagonal orthobirotunda is one of the 92 Johnson solids (J42). It consists of 10+10 triangles, 5+5 squares, and 2+10 pentagons. It can be constructed by inserting a decagonal prism between the two halves of the pentagonal orthobirotunda.

Vertex coordinates[edit | edit source]

An elongated pentagonal orthobirotunda of edge length 1 has the following vertices:

External links[edit | edit source]