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 and star polygons.
Branko Grünbaum identified two primary definitions used by
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
, one being the
regular star polygons with
intersecting edges that don't generate new vertices, and the second being
simple isotoxal
In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal () or edge-transitive if its symmetries act transitively on its edges. Informally, this means that there is only one type of edge to the object: given two ...
concave polygons.
The first usage is included in
polygrams which includes polygons like the
pentagram but also compound figures like the
hexagram
, can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green).
A hexagram ( Greek language, Greek) or sexagram (Latin) is a six-pointed ...
.
One definition of a ''star polygon'', used in
turtle graphics, is a polygon having 2 or more
turns (
turning number and
density), like in
spirolateral
In Euclidean geometry, a spirolateral is a polygon created by a sequence of fixed vertex internal angles and sequential edge lengths 1,2,3,…,''n'' which repeat until the figure closes. The number of repeats needed is called its cycles. Gardner, M ...
s.
[Abelson, Harold, diSessa, Andera, 1980, ''Turtle Geometry'', MIT Press, p.24]
Etymology
Star polygon names combine a
numeral prefix, such as ''
penta-
Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example:
* unicycle, bicycle, tricycle (1-cycle, 2-cycle, 3-cy ...
'', with the
Greek suffix ''
-gram
{{Short pages monitor