But just now I asked it to
One kinda funny thing about this type is that it does actually contain a (countably) infinite family of values. But there's no way to tell any of them from any of the others.
Last time I looked to see if Spotify had George Crumb's Vox Balaenae, it didn't, but now it does.
Mmm, they now have Harry Partch also.
Considering the dodecahedron as a graph with 20 vertices and 30 edges, it's not hard to find a hamiltonian cycle on the dodecahedron. This is a path along the edges of the dodecahedron from vertex to vertex that visits each vertex exactly once and returns to its starting point.
Such a path tontains 20 of the 30 edges, and it turns out that one can color the 30 edges in three colors so that the union of the edges in any two of the three colors forms a hamiltonian cycle.
Or, put another way, the double dodecahedron graph, with 20 vertices and 60 edges, is a union of three 20-cycles.