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The regular decagon is constructible 10-sided regular polygon with Schläfli symbol {10}. The inradius r, circumradius R, and area can be computed directly from the formulas ...

The generalized Petersen graph GP(n,k), also denoted P(n,k) (Biggs 1993, p. 119; Pemmaraju and Skiena 2003, p. 215), for n>=3 and 1<=k<=|_(n-1)/2_| is a connected cubic graph ...

As defined by Kyrmse, a canonical polygon is a closed polygon whose vertices lie on a point lattice and whose edges consist of vertical and horizontal steps of unit length or ...

If a plane cuts the sides AB, BC, CD, and DA of a skew quadrilateral ABCD in points P, Q, R, and S, then (AP)/(PB)·(BQ)/(QC)·(CR)/(RD)·(DS)/(SA)=1 both in magnitude and sign ...

An exterior angle beta of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2pi-alpha, where alpha is the corresponding internal ...

A hexagon is a six-sided polygon. Several special types of hexagons are illustrated above. In particular, a hexagon with vertices equally spaced around a circle and with all ...

Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices ...

The regular dodecagon, illustrated above, is the constructible 12-sided regular polygon that can be denoted using the Schläfli symbol {12}. The Australian 50-cent piece is ...

The regular nonagon is the regular polygon with nine sides and Schläfli symbol {9}. The regular nonagon cannot be constructed using the classical Greek rules of geometric ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...