Assertion: polyhedron's polygon | /r/HasProperty | self-dual
Facets:
value: topologically
type: DEGREE
value: geometrically
type: MANNER
Source sentences:
text: Every polygon is topologically self-dual (it has the same number of vertices as edges, and these are switched by duality), but will not in general be geometrically self-dual (up to rigid motion, for instance).
text: For polyhedra, it does not really matter whether it's the vertex figure or its dual, at least not for regular/uniform polyhedra, since regular polygons are self-dual.
text: I was quite surprised about the sentence "regular polygons are geometrically self-dual".
text: Regular polygons are self-dual, most regular polyhedra are not (only the regular tetrahedron is).
text: Every polygon is topologically self-dual (it has the same number of vertices as edges, and these are switched by duality), but will not in general be geometrically self-dual (up to rigid motion, for instance).