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The convexity coefficient chi(D) of a region D is the probability that the line segment connecting two random points in D is contained entirely within D. For a convex region, ...

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

A stack polyomino is a self-avoiding convex polyomino containing two adjacent corners of its minimal bounding rectangle. The number of stack polyominoes with perimeter 2n+4 ...

Let a set of vertices A in a connected graph G be called convex if for every two vertices x,y in A, the vertex set of every (x,y) graph geodesic lies completely in A. Also ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

A 100-sided polygon, virtually indistinguishable in appearance from a circle except at very high magnification.

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

Using a set of corners of a solid that lie in a plane to form the polygon vertices of a new polygon is called faceting. Such polygons may outline new faces that join to ...

The circumcenter of mass is a concept that can be defined by analogy with one of the the constructions for the geometric centroid for the case of polygons. The geometric ...

A plane figure consisting of four points, each of which is joined to two other points by a line segment (where the line segments may intersect). A quadrangle may therefore be ...