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In geometry, a star-shaped polygon is a polygonal region in the plane that is a star domain, that is, a polygon that contains a point from which the entire polygon boundary is visible. Formally, a polygon P is star-shaped if there exists a point z such that for each point p of P the segment z p ¯ {\displaystyle {\overline {zp}}} lies ...
A regular star polygon is a self-intersecting, equilateral, and equiangular polygon. A regular star polygon is denoted by its Schläfli symbol { p / q }, where p (the number of vertices) and q (the density ) are relatively prime (they share no factors) and where q ≥ 2.
This is the smallest star polygon that can be drawn in two forms, as irreducible fractions. The two heptagrams are sometimes called the heptagram (for {7/2}) and the great heptagram (for {7/3}). The previous one, the regular hexagram {6/2}, is a compound of two triangles. The smallest star polygon is the {5/2} pentagram.
A star domain (equivalently, a star-convex or star-shaped set) is not necessarily convex in the ordinary sense. An annulus is not a star domain.. In geometry, a set in the Euclidean space is called a star domain (or star-convex set, star-shaped set [1] or radially convex set) if there exists an such that for all , the line segment from to lies in .
The final stellation of the icosahedron has 2-isogonal enneagram faces. It is a 9/4 wound star polyhedron, but the vertices are not equally spaced.: The Fourth Way teachings and the Enneagram of Personality use an irregular enneagram consisting of an equilateral triangle and an irregular hexagram based on 142857.
Two classes of shape-based visual identification that are not done through geon representations, are those involved in: a) distinguishing between similar faces, and b) classifications that don’t have definite boundaries, such as that of bushes or a crumpled garment. Typically, such identifications are not viewpoint-invariant.
Deeper truncations of the square can produce isogonal (vertex-transitive) intermediate star polygon forms with equal spaced vertices and two edge lengths. A truncated square is an octagon, t{4}={8}. A quasitruncated square, inverted as {4/3}, is an octagram, t{4/3}={8/3}.
An isotoxal polygon has two vertices and one edge. There are isotoxal decagram forms, which alternates vertices at two radii. Each form has a freedom of one angle. The first is a variation of a double-wound of a pentagon {5}, and last is a variation of a double-wound of a pentagram {5/2}.