I am looking into some basic discrete mathematics and stumbled across a problem requiring to find the number of optimal routes from to directly opposite vertices in a cube and afterwards all the possible routes that do not cross any vertex more than once. I managed to answer each part, 6 optimal routes and 18 total routes. My question is, is there any formula or paper worth reading/looking at that would allow me to find the number of optimal routes and/or total routes ( without crossing any vertex more than once) for any given polyhedron?
Edit:polyhedron
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from math https://ift.tt/2zDTBXc
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