A beautiful polyhedron with 20 hexagons and 60 pentagons can be seen here: http://robertlovespi.wordpress.com/2013/11/03/a-polyhedron-with-80-faces/ . Euler formula and the corresponding Diophantine equation give a smaller possible combination: 7 hexagons and 20 pentagons adjacent by two to hexagons' vertices and by five in the pentagonal vertices. Does such a polyhedron really exist? I doubt but my only argument is "I was not able to compose it". At the same time I do know that the non-existence of polyhedra permitted by Euler equation is not elementary (cf. the not-existing polyhedron with 12 pentagons and 1 hexagon only).
2026-03-30 01:28:18.1774834098
Does a polyhedron with 7 hexagons and 20 pentagons exist?
300 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 13 Archimedean solids, none of them with your recipe.