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up vote 27 down vote favorite 12 So I was watching a video that features astronomer and topologist Cliff Stoll talking about how figures that aren't quadrilaterals can have all their angles equal 90 degrees on different surfaces. For example, on a sphere, you can create a triangle that has all of its angles equal $90^circ$ . On a pseudosphere, you can create a pentagon that has all of its angles equal $90^circ$ . Now, here's my question. Is there a surface where a hexagon with this property is possible? geometry share | cite | improve this question edited Dec 2 at 10:57 amWhy 191k 27 223 439