A small followup on yesterday's post:

The bitruncated pentatope is a four-dimensional polytope with ten facets, each in the shape of a truncated tetrahedron. Its skeleton (the graph formed by its vertices and edges) is a symmetric graph with 30 vertices, 60 edges, and four edges per vertex. As it turns out, this skeleton is isomorphic to the line graph of the Desargues graph.

The bitruncated pentatope and its skeleton, the line graph of the Desargues graph