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not allowed for geometric vertices. There is also a connection between geometric vertices and the vertices of a curve, its points of extreme curvature: in some sense the vertices of a polygon are points of infinite curvature, and if a polygon is approximated by a smooth curve, there will be a point of extreme curvature near each polygon vertex.

Of a plane tiling

A vertex of a plane tiling or tessellation is a point where three or more tiles meet;

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