Self-intersecting polygons, crossed polygons, or self-crossing polygons are
polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two ...
s some of whose
edges cross each other. They contrast with
simple polygons, whose edges never cross.
Some types of self-intersecting polygons are:
*the
crossed quadrilateral, with four edges
**the
antiparallelogram
In geometry, an antiparallelogram is a type of self-crossing quadrilateral. Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length sides, but these pairs of sides are not in general parallel. Instead, sides in the ...
, a crossed quadrilateral with alternate edges of equal length
***the
crossed rectangle
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containin ...
, an antiparallelogram whose edges are two opposite sides and the two diagonals of a
rectangle
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram contain ...
, hence having two edges parallel
*
Star polygon
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 operatio ...
s
**
pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle arou ...
, with five edges
**
heptagram, with seven edges
**
octagram
In geometry, an octagram is an eight-angled star polygon.
The name ''octagram'' combine a Greek numeral prefix, '' octa-'', with the Greek suffix '' -gram''. The ''-gram'' suffix derives from γραμμή (''grammḗ'') meaning "line".
Deta ...
, with eight edges
**
enneagram
Enneagram is a compound word derived from the Greek neoclassical stems for "nine" (''ennea'') and something "written" or "drawn" (''gramma''). Enneagram may refer to:
* Enneagram (geometry), a nine-sided star polygon with various configurations
...
or nonagram, with nine edges
**
decagram, with ten edges
**
hendecagram
In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices.
The name ''hendecagram'' combines a Greek numeral prefix, '' hendeca-'', with the Greek suffix ''-gram''. The ''hendeca-'' prefix derives fr ...
, with eleven edges
**
, with twelve edges
See also
*
List of regular polytopes and compounds#Stars
*
Complex polygon
The term ''complex polygon'' can mean two different things:
* In geometry, a polygon in the unitary plane, which has two complex dimensions.
* In computer graphics, a polygon whose boundary is not simple.
Geometry
In geometry, a complex polygo ...
{{DEFAULTSORT:Self-intersecting polygons,
Geometric shapes
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