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The edge-transitive polytopes that are not vertex-transitive
Göring, Frank ; Winter, Martin, matematik
V 3-dimenzionalnem evklidskem prostoru obstajata dva izjemna poliedra, rombski dodekaeder in rombski triakontaeder, edina znana politopa (poleg poligonov), ki sta povezavno tranzitvna, ne pa tudi ...točkovno tranzitivna. Pokažemo, da za ta dva poliedra ne obstajajo nobene podobne strukture v višjih dimenzijah, to pomeni, da v dimenziji ▫$d \geq 4$▫ povezavna tranzitivnost konveksnega politopa implicira točkovno tranzitivnost. Splošneje, podamo klasifikacijo vseh konveksnih politopov, ki imajo hkrati vse povezave iste dolžine, včrtano sfero, ki se vsake povezave dotika v eni sami točki, ter dvodelen povezavni graf. Pokažemo, da je vsak tak politop v dimenziji ▫$d \geq 4$▫ točkovno tranzitiven.
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