Pentambus

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Pentambus
Rank2
TypeIsotopic
Notation
Coxeter diagramm5m ()
Elements
Edges10
Vertices5+5
Vertex figureDyad
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[edit | edit source]

Star pentambus
Rank2
TypeIsotopic
Notation
Schläfli symbol
Elements
Edges10
Vertices5+5
Measures (edge length 1)
Central density1
Related polytopes
Convex hullPentagon, edge length
Convex corePentagon, edge length
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[edit | edit source]

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

  • ,
  • ,
  • ,
  • ,
  • ,
  • .