The 600-cell graph is the skeleton of the 600-cell. It has 120 vertices and 720 edges.
Several drawings are illustrated above. It is a regular
graph of degree 12, girth
3, and graph diameter 5. The numbers of vertices
at graph distance 
, 1, 2, ... from a given graph
vertex on the 600-cell graph are 1, 12, 32, 42, 32, and 1 (OEIS A118785).
The graph spectrum of the 600-cell graph is ![12^1[3(1+/-sqrt(5))]^4[2(1+/-sqrt(5))]^9(+/-3)^(16)0^(25)(-2)^(36)](/images/equations/600-CellGraph/Inline2.svg)
(Buekenhout and Parker 1998). The 600-cell graph is implemented in the Wolfram
Language as GraphData["SixHundredCellGraph"].
The independence number of the 600-cell graph is 24 (Debroni et al. 2013) and its chromatic number is 5 (R. Pratt, pers. comm., Dec. 2, 2011).
Its graph automorphism group has order 
(Buekenhout and Parker 1998).
." Disc. Math. 186, 69-94, 1998.Debroni,
S.; Delisle, E.; Myrvold, W.; Sethi, A.; Whitney, J.; Woodcock, J.; Fowler, P. W.;
de La Vaissière, B.; and Deza, M. "Maximum Independent Sets of the 120-Cell
and Other Regular Polytopes." Ars Math. Contemp. 6, 197-210, 2013.