The crossed elongated square gyrobicupola graph is the crossed graph of the elongated square gyrobicupola, obtained by joining every pair of vertices lying on a common face of the polyhedron. It is the 24-Fabrici-Madaras graph, the 24-vertex member of the Fabrici-Madaras graphs constructed by Fabrici and Madaras (2007) to show that the upper bound of 7 on the minimum vertex degree of a 1-planar graph is sharp.
The graph has 24 vertices and 84 edges, is a 7-regular graph, and has girth 3. It is Hamiltonian. Its graph crossing number and rectilinear crossing number are both 18. It is indexed as graph 50006 in the House of Graphs.
In the Wolfram Language, the graph is implemented as GraphData["CrossedElongatedSquareGyrobicupolaGraph"].
