Pentagonal-pentagrammic coil

The  is a regular skew polygon in 4-dimensional Euclidean space. It is one of 3 regular pentagons in Euclidean space, the other two being the pentagon and the pentagram.

It is the Petrie polygon of the pentachoron, consisting of a skew subset of 5 of its 10 edges.

Vertex coordinates
Its vertex coordinates are the same as those of the 4-simplex, and more generally any 5-2 step prism.

Related polytopes
The is the vertex figure of the skew icosahedron.