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.

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.