The skeleton of the bislit cube is the 8-vertex simple graph, illustrated above in several embeddings, which consists of a cube in which two
opposite faces have polyhedron diagonals oriented
perpendicular to each other. It is the dual
graph of the skeleton of the gyrobifastigium
(Johnson solid 
).
It is implemented in the Wolfram Language as GraphData["BislitCube"].
The plots above show the adjacency, incidence, and distance matrices of the bislit cube graph.
