# Pentapod

Pentapod
Rank2
TypeSemi-uniform
Notation
Bowers style acronymPepod
Coxeter diagramx5/4y
Elements
Edges5+5
Vertices10
Measures (edge lengths a , b )
Circumradius${\displaystyle {\sqrt {\frac {5a^{2}+5b^{2}-5ab+(a^{2}+b^{2}-3ab){\sqrt {5}}}{10}}}}$
Angle36°
Related polytopes
ArmyDipeg
DualConcave pentambus
Abstract & topological properties
Flag count20
OrientableYes
Properties
SymmetryH2, order 10
ConvexNo
NatureTame

The pentapod is a semi-uniform polygon that has 10 sides of two different edge lengths. The angles of a pentapod are always 36 degrees. It is a faceting of the dipentagon.

A pentapod generally has the Coxeter diagram x5/4y, where the ratio between the two edge classes is greater than ${\displaystyle {\frac {1+{\sqrt {5}}}{2}}}$. If the ratio is less than this value, another semi-uniform polygon called the distellagon results. If the edge ratio is exactly ${\displaystyle {\frac {1+{\sqrt {5}}}{2}}}$, the degenerate complex dipentagon forms, which looks like a pentagon and pentagram sharing the same vertex set.