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It seems to me that
- If it is distance-regular, it must be edge-transitive.
- If it the skeleton of a regular polytope, it must be vertex-transitive.
- If it is edge-transitive and vertex-transitive, it must be symmetric.
Does this qualify as "original research", or can I add "symmetric" to its infobox? Maproom (talk) 17:36, 22 August 2015 (UTC)