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24-Cell Graph

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24CellGraphs

The 24-cell graph is the skeleton of the 24-cell. It is an octic graph on 24 vertices and 96 edges, illustrated above in three projective drawings and three order-3 LCF notation drawings.

The 24-cell graph has girth 3, graph diameter 3, and graph genus 6 (E. Weisstein, Jan. 13, 2026). It is an integral graph with graph spectrum (-4)^2(-2)^80^94^48^1 (Buekenhout and Parker 1998).

Its graph automorphism group has order |Aut(G)|=2^7·3^2=1152 (Buekenhout and Parker 1998).

The 24-cell graph is implemented in the Wolfram Language as GraphData["TwentyFourCellGraph"].

See also

16-Cell Graph, 24-Cell, 120-Cell Graph, 600-Cell Graph, Integral Graph, Octic Graph

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References

Buekenhout, F. and Parker, M. "The Number of Nets of the Regular Convex Polytopes in Dimension <=4." Disc. Math. 186, 69-94, 1998.House of Graphs. "Twenty Four Cell Graph." https://houseofgraphs.org/graphs/1401.

Cite this as:

Weisstein, Eric W. "24-Cell Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/24-CellGraph.html

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