A crossed graph is the name given by Brandenburg (2021) 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 | crossed elongated square gyrobicupola graph | Fabrici and Madaras (2007) |
| regular dodecahedron | crossed dodecahedral graph | Brandenburg (2021) |
| icosidodecahedron | icosahedral line graph | |
| rhombic dodecahedron | crossed rhombic dodecahedral graph | |
| truncated tetrahedron | circulant graph  |
A different use of "crossed graph" appears in the notion of the crossed prism graph adopted in this work.
