# Pentambus

Pentambus
Rank2
TypeIsotopic
Notation
Coxeter diagramm5m ()
Elements
Edges10
Vertices5+5
Measures (edge length 1)
Central density1
Related polytopes
DualDipentagon
Abstract & topological properties
Flag count20
Euler characteristic0
OrientableYes
Properties
SymmetryH2, order 10
Flag orbits2
ConvexYes
NatureTame

The pentambus is a non-regular equilateral decagon with pentagonal symmetry. It has 10 edges of equal length, with 2 alternating angles. The two alternating angles in a pentambus add up to 288°.

## Star pentambus

Star pentambus
Rank2
TypeIsotopic
Notation
Schläfli symbol${\displaystyle \mid 5/2\mid }$
${\displaystyle \left\{5_{36^{\circ }}\right\}}$
Elements
Edges10
Vertices5+5
Measures (edge length 1)
Central density1
Related polytopes
Convex hullPentagon, edge length ${\displaystyle {\dfrac {1+{\sqrt {5}}}{2}}}$
Convex corePentagon, edge length ${\displaystyle {\dfrac {1-{\sqrt {5}}}{3}}}$
Abstract & topological properties
Flag count20
Euler characteristic0
OrientableYes
Properties
SymmetryH2, order 10
Flag orbits2
ConvexNo
NatureWild

The star pentambus is a variant of the pentambus which resembles the pentagram. It can be constructed from a pentagram by adding vertex at the points of self intersection, and replacing the edges with only the external pieces.

### Vertex coordinates

Vertex coordinates for a star pentambus of unit edge length centered at the origin can be given as:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}},\,-{\sqrt {\frac {25+11{\sqrt {5}}}{40}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {3+{\sqrt {5}}}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}}\right)}$,
• ${\displaystyle \left(0,\,{\sqrt {\frac {5+2{\sqrt {5}}}{5}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}}\right)}$,
• ${\displaystyle \left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)}$.