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Brief facts about pentagon shape:

In geometry, a pentagon is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon is called a pentagram.

Associahedron ; A pentagon is an order-4 associahedron.

Dodecahedron , a polyhedron whose regular form is composed of 12 pentagonal faces.

Golden ratio - In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0,.

Pentagonal number s

Pentagram - A pentagram is a regular five-pointed star polygon, formed from the diagonal line segments of a convex regular pentagon.

Pentagram map - In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections.

Constructible polygons