Polygon

In general, a polygon is a 2D plane figure enclosed by a finite number of connected straight line segments of any form.

Name of a Polygon

Usually, a polygon is named according to the number of sides

List of Named Polygons

SidesNameRemarks 1monogon 2digon 3triangle/trigon 4quadrilateral/tetragon 5pentagon 6hexagon 7heptagon/septagon 8octagon 9nonagon/enneagon 10decagon 11hendecagon/undecagon 12dodecagon/duodecagon 13tridecagon/triskaidecagon 14tetradecagon/tetrakaidecagon 15pentadecagon/pentakaidecagon 16hexadecagon/hexakaidecagon 17heptadecagon/heptakaidecagon 18octadecagon/octakaidecagon 19enneadecagon/enneakaidecagon 20icosagon 24icositetragon/icosikaitetragon 30triacontagon 40tetracontagon/tessaracontagon 50pentacontagon/pentecontagon 60hexacontagon/hexecontagon 70heptacontagon/hebdomecontagon 80octacontagon/ogdoecontagon 90enneacontagon/enenecontagon 100hectogon/hecatontagon 257257-gon 1000chiliagon 10000myriagon 6553765537-gon 1000000megagon ∞apeirogon

Naming Typical N-gons

TensmiddleOnesSuffix  -kai-1,-hena--gon 20, icosi- (icosa- when alone-kai-2, -di--gon 30, triaconta- / tessaraconta--kai-3, -tri--gon 40, tetraconta- / tessaraconta--kai-4, -tetra--gon 50, pentaconta- / penteconta--kai-5, -penta--gon 60, hexaconta- / hexeconta--kai-6, -hexa--gon 70, heptaconta- / hebdomeconta--kai-7, -hepta--gon 80, octaconta- / ogdoeconta--kai-8, -octa--gon 90, enneaconta- / eneneconta--kai-9, -ennea--gon

Classification of Polygon

Convexity and Non-convexity

Simple

Simple

the boundary of the polygon does not cross itself. All convex polygons are simple.

Convex

any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice. As a consequence, all its interior angles are less than 180°. Equivalently, any line segment with endpoints on the boundary passes through only interior points between its endpoints.

Non-convex

a line may be found which meets its boundary more than twice. Equivalently, there exists a line segment between two boundary points that passes outside the polygon.

Concave

Non-convex and simple. There is at least one interior angle greater than 180°.

Star-shaped

the whole interior is visible from at least one point, without crossing any edge. The polygon must be simple, and may be convex or concave. All convex polygons are star-shaped.

Intersectomg

Self-intersecting

the boundary of the polygon crosses itself. The term complex is sometimes used in contrast to simple, but this usage risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions.

Star polygon

a polygon which self-intersects in a regular way. A polygon cannot be both a star and star-shaped.

Equality and Symmetry

Equiangular

all corner angles are equal.

Cyclic:

all corners lie on a single circle, called the circumcircle.

Isogonal or vertex-transitive:

all corners lie within the same symmetry orbit. The polygon is also cyclic and equiangular.

Equilateral

all edges are of the same length. The polygon need not be convex.

Tangential

all sides are tangent to an inscribed circle.

Isotoxal or edge-transitive

all sides lie within the same symmetry orbit. The polygon is also equilateral and tangential.

Regular

the polygon is both isogonal and isotoxal. Equivalently, it is both cyclic and equilateral, or both equilateral and equiangular. A non-convex regular polygon is called a regular star polygon.

Irregular

Any n-gon that is not regular

Miscellaneous

Rectilinear

the polygon's sides meet at right angles, i.e., all its interior angles are 90 or 270 degrees.

Monotone

with respect to a given line L: every line orthogonal to L intersects the polygon not more than twice.

Source and Reference

• https://en.wikipedia.org/wiki/Polygon