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The symmetry group of an n-sided regular polygon is the dihedral group D n (of order 2n): D 2, D 3, D 4, ... It consists of the rotations in C n, together with reflection symmetry in n axes that pass through the center. If n is even then half of these axes pass through two opposite vertices, and the other half through the midpoint of opposite ...
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.
Octagonal zonogon Tessellation by irregular hexagonal zonogons Regular octagon tiled by squares and rhombi. In geometry, a zonogon is a centrally-symmetric, convex polygon. [1] Equivalently, it is a convex polygon whose sides can be grouped into parallel pairs with equal lengths and opposite orientations, the two-dimensional analog of a zonohedron.
A regular polygon with n sides can be constructed with ruler, compass, and angle trisector if and only if =, where r, s, k ≥ 0 and where the p i are distinct Pierpont primes greater than 3 (primes of the form +). [8]: Thm. 2 These polygons are exactly the regular polygons that can be constructed with Conic section, and the regular polygons ...
The Laves tilings have vertices at the centers of the regular polygons, and edges connecting centers of regular polygons that share an edge. The tiles of the Laves tilings are called planigons. This includes the 3 regular tiles (triangle, square and hexagon) and 8 irregular ones. [4] Each vertex has edges evenly spaced around it.
The polytopes of rank 2 (2-polytopes) are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schläfli symbol {p}. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular. They use the same vertices as the convex forms, but ...
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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 ...