Thursday, January 23, 2014

[wtdcmxpi] Better Hoffman-Singleton cards

Create a deck of 175 cards, or better yet, domino tiles, representing the edges of the graph.

Add another 50 representing the nodes.  A cheap way to do it is remove 2 cards from a regular card deck.  Or 50 Pokémon names. I think no node is special compared to any other node.

Add more cards for additional structures in the graph. Does the graph represent a polyhedron? If so, the faces could get their own cards, or sets of three consecutive vertices on each face.

Inspired by Ed Pegg's cards. Those cards have the problem that one cannot easily see connected nodes. Two early ideas: Let the cards not be physical but depicted in a computer program which can assist in seeing connections. Or, label the nodes simply (e.g., Pokémon), and simply list the 7 neighbors on each card.

Alternatively, Tutte-Coxeter graph: 30 vertices, 45 edges, cubic.

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