Complex dipentagon

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Complex dipentagon
Rank2
TypeSemi-uniform
Elements
Edges5 + 5
Vertices5
Vertex figureTetrad
Measures (minor edge length 1)
Edge lengthsPentagonal edges (5): 1
 Pentagrammic edges (5):
Circumradius
Perimeter
Central density3
Related polytopes
ArmyPeg
DualMermin's pentagram
ConjugateComplex dipentagon
Convex corePentagon
Abstract & topological properties
Flag count20
Configuration symbol(54, 102)
SkeletonK5
Properties
SymmetryH2, order 10
ConvexNo
NatureExotic

The complex dipentagon is a semi-uniform exotic polygonoid. It has 10 edges of two different lengths, with 2 of each at a vertex making a tetrad vertex figure. It is semi-uniform, however if conjugacies are included in its symmetry it becomes regular.

It can be seen as a compound of a pentagon and a pentagram, with their vertices coinciding and merging into tetradic vertices.

Related polytopoids[edit | edit source]

As a vertex figure[edit | edit source]

The complex dipentagon appears as the vertex figure of both the small complex icosidodecahedron and the great complex icosidodecahedron