regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons...

Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...

In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not...

solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polygons and...

or at least one angle is 180°. Thus a degenerate convex polygon of n sides looks like a polygon with fewer sides. In the case of triangles, this definition...

even-sided. Regular skew polygons in 3 dimensions (and regular skew apeirogons in two dimensions) are always zig-zag. A regular skew polygon is a faithful...

disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides...

the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a regular polyhedron is a skew polygon such that every two consecutive...

In geometry, an affine-regular polygon or affinely regular polygon is a polygon that is related to a regular polygon by an affine transformation. Affine...

apeiros 'infinite, boundless' and γωνία gonia 'angle') or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case...

mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible...

it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be...

a regular polygon. The polytopes of rank 2 (2-polytopes) are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is...

perimeter of an equilateral polygon, one must multiply the common length of the sides by the number of sides. A regular polygon may be characterized by the...

of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle...

regular convex polygon, the regular convex pentagon has an inscribed circle. The apothem, which is the radius r of the inscribed circle, of a regular...

does then it is a regular polygon. If the number of sides is at least four, an equilateral polygon does not need to be a convex polygon: it could be concave...

solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon (regular pyramids)...

circle-like polygon with one million sides (mega-, from the Greek μέγας, meaning "great", being a unit prefix denoting a factor of one million). A regular megagon...

polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number...

one is that the faces are congruent regular polygons which are assembled in the same way around each vertex. A regular polyhedron is identified by its Schläfli...

Reuleaux polygon. As a special case, this construction is possible for every regular polygon with an odd number of sides. Every Reuleaux polygon must have...

and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen. The convex regular 4-polytopes...

points lie at the vertices of a regular polygon centered on the origin. Three real projections of regular complex polygon 4{4}2 are illustrated above, with...

angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. A regular hexagon is defined as...

outer circle that passes through each vertex of the polygon. All triangles and all regular polygons are bicentric. On the other hand, a rectangle with...

hexagon, which does not necessarily have opposite sides parallel. If a polygon is regular (both equiangular and equilateral), the sum of the distances to the...

hyperbolic geometry both lack polygons with four equal sides and right angles, they have square-like regular polygons with four sides and other angles...

Every regular polygon is a cyclic polygon. For a cyclic polygon with an odd number of sides, all angles are equal if and only if the polygon is regular. A...

regular polygons, apeirogons and regular star polygons are isogonal. The dual of an isogonal polygon is an isotoxal polygon. Some even-sided polygons...