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In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. [1] The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
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.
This condition is true for polygons in any geometry, not just Euclidean. [2] Non-convex: a line may be found which meets its boundary more than twice. Equivalently, there exists a line segment between two boundary points that passes outside the polygon. Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
When the tessellation is made of regular polygons, the most common notation is the vertex configuration, which is simply a list of the number of sides of the polygons around a vertex. The square tiling has a vertex configuration of 4.4.4.4, or 4 4. The tiling of regular hexagons is noted 6.6.6, or 6 3. [18]
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 ...
[2]: p. 1 They could also construct half of a given angle, a square whose area is twice that of another square, a square having the same area as a given polygon, and regular polygons of 3, 4, or 5 sides [2]: p. xi (or one with twice the number of sides of a given polygon [2]: pp. 49–50 ).
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 ...