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Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...

A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...

The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

The word "star" is used in a number of different ways in mathematics. The term is commonly used to voice an asterisk when appearing in a mathematical expression. For example, ...

A centered polygonal number consisting of a central dot with four dots around it, and then additional dots in the gaps between adjacent dots. The general term is n^2+(n+1)^2, ...

A centered triangular number is a centered polygonal number consisting of a central dot with three dots around it, and then additional dots in the gaps between adjacent dots. ...

A polygonal number of the form n(5n-3)/2. The first few are 1, 7, 18, 34, 55, 81, 112, ... (OEIS A000566). The generating function for the heptagonal numbers is ...

A polygonal number of the form O_n=n(3n-2). The first few are 1, 8, 21, 40, 65, 96, 133, 176, ... (OEIS A000567). The generating function for the octagonal numbers is ...

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of a ...

Given a Schwarz triangle (p q r), replacing each polygon vertex with its antipodes gives the three colunar spherical triangles (p q^' r^'),(p^' q r^'),(p^' q^' r), (1) where ...