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For example, <6-2> is a hexagon with 90° internal angles of the difference, <4>, 1 counter-turned vertex. A multiturn indirect equilateral p-gon can be given the notation < p-2c / q > with c counter turn vertices, and q total turns. An equiangular polygon <p-p> is a p-gon with undefined internal angles θ, but can be expressed explicitly as <p ...
Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram - star polygon with 9 sides; Decagram - star polygon with 10 sides; Hendecagram - star polygon with 11 sides; Dodecagram - star polygon with 12 sides; Apeirogon - generalized polygon with countably infinite ...
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
For example, {6/2} may be treated in either of two ways: For much of the 20th century (see for example Coxeter (1948) ), we have commonly taken the /2 to indicate joining each vertex of a convex {6} to its near neighbors two steps away, to obtain the regular compound of two triangles, or hexagram .
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because 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 by modern definition, creating more special properties.
Equilateral: all edges are of the same length. Regular: both equilateral and equiangular. Cyclic: all corners lie on a single circle, called the circumcircle. Tangential: all sides are tangent to an inscribed circle. Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The polygon is also cyclic and equiangular.
For example, {3} is an equilateral triangle, {4} is a square, {5} a convex regular pentagon, etc. Regular star polygons are not convex, and their Schläfli symbols { p / q } contain irreducible fractions p / q , where p is the number of vertices, and q is their turning number .
A rectangle is a rectilinear polygon: its sides meet at right angles. A rectangle in the plane can be defined by five independent degrees of freedom consisting, for example, of three for position (comprising two of translation and one of rotation), one for shape (aspect ratio), and one for overall size (area).