Why can't you cover spherical surface with quads so that 4 lines meet at every vertex? How would the proof of that look?
> If you want only quadrilaterals, and you want most vertices to be a meeting between 4 quadrilaterals, but some places 3 quadrilaterals meet, you can use the Euler characteristic to deduce that there must be 8 of these degenerate vertices.
https://math.stackexchange.com/a/4904806
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> If you want only quadrilaterals, and you want most vertices to be a meeting between 4 quadrilaterals, but some places 3 quadrilaterals meet, you can use the Euler characteristic to deduce that there must be 8 of these degenerate vertices.
https://math.stackexchange.com/a/4904806