# Odd-4 Graph, Fano Planes, and the Coxeter Graph

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The odd-4 graph is constructed by taking triplets from {1, 2, 3, 4, 5, 6, 7}, then connecting the triplets that share no values. Ignoring the colored edges, the entire 35-vertex graph is the odd-4 graph. The odd-3 graph is the Petersen graph, and the odd-2 graph is the pentagon.

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Contributed by: Ed Pegg Jr (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Late in his career, Coxeter saw this graph in a technical paper, and found several interesting properties about it. He asked his assistant Asia what it was called. "You discovered it, 30 years ago. It's popularly called the Coxeter graph." Coxeter then wrote up a paper, "My Graph".

## Permanent Citation

"Odd-4 Graph, Fano Planes, and the Coxeter Graph"

http://demonstrations.wolfram.com/Odd4GraphFanoPlanesAndTheCoxeterGraph/

Wolfram Demonstrations Project

Published: March 7 2011