Investigations of a hybrid Gewirtz and Peterson graph
Take a Gewirtz Graph which has 56 vertices each with degree 10, and substitite each Gewirtz vertex with a Petersen Graph which has 10 vertices each with degree 3. Each of the ten Gewirtz edges for a substituted vertex connects to a distinct node of the Petesen graph, such that each of the Petersen vertices goes from degree three to degree four. This gives a regular graph with 560 vertices of degree 4.
The resulting structure seems quite interesting.