complete graph K37, laser etched.

With Ike Feitler‘s help:

The complete graph K_{37}, laser etched on acrylic. There
is an svg of the design at thingiverse, so if you have a laser etcher, you can make it yourself.

According to Wolfram Alpha, K_{37} is
arc-transitive, biconnected, bridgeless, cage, Cayley graph, chromatically unique, circulant, claw-free , complete, connected, cyclic, determined by spectrum, distance-regular, distance-transitive, edge-transitive, Hamilton-connected, Hamiltonian, Hamming, integral, Johnson, Kneser, LCF, line graph, nonplanar, perfect, regular, strongly regular, symmetric, traceable, Turán, unitransitive, and vertex-transitive. (links will come with a future edit to this post).

It has graph spectrum (-1)^{36}36^{1} and 666 (spooky!) edges. The graph stability index is 1.203 trillion.

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