Search results
Results From The WOW.Com Content Network
A regular hexagon has Schläfli symbol {6}. A regular hexagon is a part of the regular hexagonal tiling, {6,3}, with three hexagonal faces around each vertex. A regular hexagon can also be created as a truncated equilateral triangle, with Schläfli symbol t{3}.
These properties apply to all regular polygons, whether convex or star: A regular n-sided polygon has rotational symmetry of order n. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon.
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
A skew polygon does not lie in a flat plane, but zigzags in three (or more) dimensions. The Petrie polygons of the regular polytopes are well known examples. An apeirogon is an infinite sequence of sides and angles, which is not closed but has no ends because it extends indefinitely in both directions.
For example, the Schläfli symbol for an equilateral triangle is {3}, while that for a square is {4}. [20] The Schläfli notation makes it possible to describe tilings compactly. For example, a tiling of regular hexagons has three six-sided polygons at each vertex, so its Schläfli symbol is {6,3}. [21]
In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also include 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 divided into two ...
In mathematics, a dihedral group is the group of symmetries of a regular polygon, [1] [2] which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. [3] The notation for the dihedral group differs in geometry and abstract ...
A regular hexagram, , can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram ( Greek ) or sexagram ( Latin ) is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}.