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Timeline for 3D analog of the Petersen graph

Current License: CC BY-SA 4.0

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Feb 4, 2023 at 18:56 answer added S. Carnahan timeline score: 7
Feb 4, 2023 at 7:15 comment added verret @Daniel Sebald : there is no edge-transitive graph of order $24$ with automorphism group of order $1440$ either. There are only $65$ connected edge-transitive graphs of order $24$, so maybe you could check them to see if anything looks like what you are after?
Feb 4, 2023 at 6:15 history edited Daniel Sebald CC BY-SA 4.0
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Feb 4, 2023 at 0:37 comment added verret Thanks for the correction. Here's another attempt: according to math.auckland.ac.nz/~conder/AllSmallETgraphs-upto47-summary.txt, there is no edge-transitive graph of order $24$ with automorphism group $2880$.
Feb 2, 2023 at 18:23 comment added Andreas Blass @verret I understood the suggested graph to have 24 vertices, just as the Petersen graph has 10 vertices, not 5.
Feb 2, 2023 at 18:14 comment added verret I think all the polyhedron you suggested have 12 vertices, but there is no transitive group of order 2880 and degree 12. (But there are some such groups of degree 20.)
Feb 2, 2023 at 17:41 history asked Daniel Sebald CC BY-SA 4.0