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A polygon vertex x_i of a simple polygon P is a principal polygon vertex if the diagonal [x_(i-1),x_(i+1)] intersects the boundary of P only at x_(i-1) and x_(i+1).

A quantitative measure of the simplicity of a geometric construction which reduces geometric constructions to five steps. It was devised by È. Lemoine. S_1 Place a ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

A random polygon containing the origin (Kovalenko 1999).

The edge of a polygon or face of a polyhedron are sometimes called sides.

Except for convex polygons, every simple polygon has at least one mouth.

Except for triangles, every simple polygon has at least two nonoverlapping ears.

A conformal mapping from the upper half-plane to a polygon.

A dodecagon is a 12-sided polygon. Several special types of dodecagons are illustrated above. In particular, a dodecagon with vertices equally spaced around a circle and with ...

The digon is the degenerate polygon (corresponding to a line segment) with Schläfli symbol {2}.