DOWNLOAD-DESKTOP-NOTEBOOK.nb (3.3 MB)
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In my talk, I promised that the order 6 dominator graph could be done nicely.
\[Phi] = 1/2 (1 + Sqrt[5]);
icosidodecahedron =
Join @@ (ResourceFunction["SignedPermutations"][#, "Even"] & /@ {{0,
0, \[Phi]}, {1, \[Phi], \[Phi]^2}/2});
coord = icosidodecahedron[[{1, 8, 15, 21, 14, 2, 9, 20, 18, 11, 13,
12, 25, 24, 6, 22, 17, 28, 3, 23, 16, 19, 29, 4, 26, 7, 10, 5, 30,
27}]];
vert = StringJoin[ToString /@ #] & /@
Select[Tuples[Range[6], {2}], Length[Union[#]] == 2 &];
edge = (StringJoin[ToString /@ #] & /@ Partition[#, 2, 1]) & /@
Select[Tuples[Range[6], {3}], Length[Union[#]] == 3 &];
at30d = Graph3D[DirectedEdge @@@ edge,
VertexCoordinates -> Thread[vert -> coord],
VertexLabels -> Placed[Automatic, Center], VertexSize -> .2]
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