A crossed graph is the name given by Brandenburg to a graph obtained from a polyhedron by drawing edges between every pair of vertices in all its faces. This process leaves triangular faces unchanged. The following table summarizes some special cases. base polyhedron | crossed graph | reference cube | 16-cell graph | cuboctahedron | octahedral line graph | elongated square gyrobicupola | elongated square gyrorocupola graph | Fabrici and Madaras regular dodecahedron | crossed dodecahedral graph | Brandenburg icosidodecahedron | icosahedral line graph | rhombic dodecahedron | crossed rhombic dodecahedron | truncated tetrahedron | circulant graph C i_12(1, 2, 4, 5, 6) |

crossed prism graph | polyhedron | skeleton