Shadow Abstract :Icosidodecahedron to PentagonalOrthobirotunda:
This started as looking for a 30 vertex polyhedron I could hang 31 hexagons on for 5^2+5+1 5th order projective plane,
but I found this strange polyhedral dual the Icosidodecahedron and PentagonalOrthobirotunda.
The edge switch of these two make a natural Abstract.
The Shadow Abstract was the result.
Pictures:

https://scontent-lax3-1.xx.fbcdn.net/v/t39.30808-6/427462493_101615...