The proof that there exists only five platonic solids assumes that the angle between the adjacent sides must be less than 360°, because otherwise the surfaces would be flat or even overlap. However this proof doesn't seem to work in non-euclidean space, because the sum of angles of the sides to generate a "flat" surface could be higher or lower than 360°.
Does this mean that the number of platonic solids in non-euclidean or curved space could be different from five?