Complex dipentagon

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.

Dual
The dual configuration of the complex dipentagon is a configuration with tetradic edges and dyadic vertex figures. It can be realized in Euclidean space with the same symmetry as the complex dipentagon.

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