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A truncated hexagon, t{6}, is a dodecagon, {12}, alternating two types (colors) of edges. An alternated hexagon, h{6}, is an equilateral triangle, {3}. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. A regular hexagon can be dissected into six equilateral triangles by adding a
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
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 hexadecagram is a 16-sided star polygon, represented by symbol {16/n}. There are three regular star polygons , {16/3}, {16/5}, {16/7}, using the same vertices, but connecting every third, fifth or seventh points.
The area A of a convex regular n-sided polygon having side s, circumradius R, ... and icosahedron) have Petrie polygons, seen in red here, with sides 4, 6, 6, 10, ...
The area formula can also be applied to self-overlapping polygons since the meaning of area is still clear even though self-overlapping polygons are not generally simple. [6] Furthermore, a self-overlapping polygon can have multiple "interpretations" but the Shoelace formula can be used to show that the polygon's area is the same regardless of ...
In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular dodecagon, m=6, and it can be divided into 15: 3 squares, 6 wide 30° rhombs and 6 narrow 15° rhombs. This decomposition is based on a Petrie polygon projection of a 6-cube, with 15 of 240 faces
The area can be also expressed in terms of bimedians as [16] = , where the lengths of the bimedians are m and n and the angle between them is φ. Bretschneider's formula [17] [14] expresses the area in terms of the sides and two opposite angles: