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Here is a graph that appeared in an analysis I am doing for quaternion triple products: enter image description here

There are three pairs of vertices that are not connected, so this graph is not $K_{3,3}$ which needs two pairs of triplets. The extra vertices happen to be 1q1 at the center, iqi, jqj, and kqk on the triangle, and (1qi, 1qj, 1qk, iq1, jq1, kq1) which does form the graph $K_{3,3}$ as people answering my last question pointed out. The vertices in use I call the cross gammas, and are (iqj, iqk, jqk, jqi, kqi, kqj). I know people like to study antisymmetric math structures, so it might tie into something well-studied that way.

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up vote 2 down vote accepted

It's the graph given by the vertices and edges of a (triangular) prism.

EDIT: Also, it's the 1st graph in the 1st diagram at

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Spot on. Thanks for the additional link. – sweetser Jun 18 '11 at 10:32

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