A regular star pentagon, {5/2}, has five vertices (its corner tips) and five intersecting edges, while a concave decagon, |5/2|, has ten edges and two sets of five vertices. The first is used in definitions of star polyhedra and star uniform tilings, while the second is sometimes used in planar tilings.
Small stellated dodecahedron
Tessellation
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations on regular simple or star polygons.
Branko Grünbaum identified two primary usages of this terminology by Johannes Kepler, one corresponding to the regular star polygons with intersecting edges that do not generate new vertices, and the other one to the isotoxal concave simple polygons.[1]
Polygrams include polygons like the pentagram, but also compound figures like the hexagram.
One definition of a star polygon, used in turtle graphics, is a polygon having q ≥ 2 turns (q is called the turning number or density), like in spirolaterals.[2]
^Grünbaum & Shephard (1987). Tilings and Patterns. Section 2.5
^Abelson, Harold, diSessa, Andera, 1980, Turtle Geometry, MIT Press, p. 24
In geometry, a starpolygon is a type of non-convex polygon. Regular starpolygons have been studied in depth; while starpolygons in general appear not...
solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating starpolygons and...
length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates...
(sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed starpolygon, formed from the diagonal line segments of a convex...
Starpolygons and polygonal compounds are the basis for numerous figures of significance in arts and culture. The figure may be the border or interior...
two triangles. The smallest starpolygon is the {5/2} pentagram. The next one is the {8/3} octagram and its related {8/2} star figure (a compound of two...
star domain but is not convex. A star-shaped polygon is a star domain whose boundary is a sequence of connected line segments. The closure of a star domain...
Wiktionary, the free dictionary. In geometry, an octagram is an eight-angled starpolygon. The name octagram combine a Greek numeral prefix, octa-, with the Greek...
figure 8, infinity symbol, or lemniscate curve. Crossed polygons are related to starpolygons which have turning numbers greater than 1. The vertices...
In geometry, a covering of a polygon is a set of primitive units (e.g. squares) whose union equals the polygon. A polygon covering problem is a problem...
There are also an infinite number of regular star dihedra and hosohedra {2,p/q} and {p/q,2} for any starpolygon {p/q}. While degenerate in Euclidean space...
polyhedron can contain either starpolygon faces, starpolygon vertex figures, or both. The complete set of 57 nonprismatic uniform star polyhedra includes the...
In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees. The regular icosagon has Schläfli...
A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}. Since there are no true regular...
ten-pointed starpolygon Hendecagram, an eleven-pointed starpolygon Dodecagram, a twelve-pointed starpolygon Magic star, a starpolygon in which numbers...
An n-pointed magic star is a starpolygon with Schläfli symbol {n/2} in which numbers are placed at each of the n vertices and n intersections, such that...
represented by Schläfli symbol {p}. Many sources only consider convex polygons, but starpolygons, like the pentagram, when considered, can also be regular. They...
geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon. A regular tetradecagon has Schläfli symbol {14} and can be constructed...
duals to form five-dimensional antiprisms. Uniform star antiprisms are named by their starpolygon bases, {p/q}, and exist in prograde and in retrograde...
In geometry, an angle of a polygon is formed by two adjacent sides. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or...
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