Assertion: polyhedron's vertex | /r/HasProperty | regular
Facets:
Source sentences:
text: If the vertex figure is a regular polygon, then the vertex itself is said to be regular.
text: (This implies that every face is the same regular polygon; it also implies that every vertex is regular.)
text: A quasi-regular dual is face-transitive and edge-transitive (and hence every vertex is regular) but not vertex-transitive.
text: A semi-regular dual is face-transitive but not vertex-transitive, and every vertex is regular.
text: The vertex is said to be regular if this is a regular polygon and symmetrical with respect to the whole polyhedron.
text: ; it also implies that every vertex is regular).
text: if it is vertex-transitive, edge-transitive and face-transitive (this implies that every face is the same regular polygon; it also implies that every vertex is regular).
text: A quasi-regular dual is face-transitive and edge-transitive (and hence every vertex is regular) but not vertex-transitive.
text: A is face-transitive and edge-transitive (and hence every vertex is regular) but not vertex-transitive.
text: A semi-regular dual is face-transitive but not vertex-transitive, and every vertex is regular.
text: A is face-transitive but not vertex-transitive, and every vertex is regular.