This is a list of

two-dimensional A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimension ...

geometric shape A shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type. In geometry, ''shape'' excludes informat ...

s in Euclidean and other

geometries Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Types, methodologies, and terminologies of geometry. ...

. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.

Generally composed of straight line segments

Angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...

* Balbis *

Concave polygon A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180° degrees and 360° degrees exclusive. ...

Constructible polygon In mathematics, a constructible polygon is a regular polygon that can be Compass and straightedge constructions, constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regu ...

Convex polygon In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is ...

Cyclic polygon In geometry, a set (mathematics), set of point (geometry), points are said to be concyclic (or cocyclic) if they lie on a common circle. A polygon whose vertex (geometry), vertices are concyclic is called a cyclic polygon, and the circle is cal ...

Equiangular polygon In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral polygon, equilateral) then it is a regular polygon. Isogonal polygons are equi ...

Equilateral polygon In geometry, an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, an equilateral polygon does not need to also be equiangular (have all angles equal), but if it does then it is a regular polygon ...

* Penrose tile *

Polyform In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a trian ...

Regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex ...

Simple polygon In geometry, a simple polygon is a polygon that does not Intersection (Euclidean geometry), intersect itself and has no holes. That is, it is a Piecewise linear curve, piecewise-linear Jordan curve consisting of finitely many line segments. The ...

Tangential polygon In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an ''incircle''). This is a circle that is tangent to each of the polygon's sides. The dual po ...

Polygons with specific numbers of sides

Triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

– 3 sides **

Acute triangle An acute triangle (or acute-angled triangle) is a triangle with three ''acute angles'' (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one ''obtuse angle'' (greater than 90°) and two acute angles. Since a triang ...

Equilateral triangle An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the ...

** Heptagonal triangle **

Isosceles triangle In geometry, an isosceles triangle () is a triangle that has two Edge (geometry), sides of equal length and two angles of equal measure. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at le ...

*** Golden Triangle **

Obtuse triangle An acute triangle (or acute-angled triangle) is a triangle with three ''acute angles'' (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one '' obtuse angle'' (greater than 90°) and two acute angles. Since a trian ...

Rational triangle An integer triangle or integral triangle is a triangle all of whose side lengths are integers. A rational triangle is one whose side lengths are rational numbers; any rational triangle can be rescaled by the lowest common denominator of the s ...

** Heronian triangle *** Pythagorean triangle *** Isosceles heronian triangle *** Primitive Heronian triangle **

Right triangle A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle ( turn or 90 degrees). The side opposite to the right angle i ...

*** 30-60-90 triangle ***

Isosceles right triangle A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°� ...

*** Kepler triangle **

Scalene triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional ...

Quadrilateral In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''l ...

– 4 sides **

Cyclic quadrilateral In geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral (four-sided polygon) whose vertex (geometry), vertices all lie on a single circle, making the sides Chord (geometry), chords of the circle. This circle is called ...

Kite A kite is a tethered heavier than air flight, heavier-than-air craft with wing surfaces that react against the air to create Lift (force), lift and Drag (physics), drag forces. A kite consists of wings, tethers and anchors. Kites often have ...

***

Rectangle In Euclidean geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that a ...

***

Rhomboid Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. The terms "rhomboid" and "parallelogram" are often erroneously conflated with each oth ...

***

Rhombus In plane Euclidean geometry, a rhombus (: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhom ...

***

Square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

(regular quadrilateral) **

Tangential quadrilateral In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex polygon, convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral. This cir ...

Trapezoid In geometry, a trapezoid () in North American English, or trapezium () in British English, is a quadrilateral that has at least one pair of parallel sides. The parallel sides are called the ''bases'' of the trapezoid. The other two sides are ...

***

Isosceles trapezoid In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and bo ...

Trapezus Trabzon, historically known as Trebizond, is a city on the Black Sea coast of northeastern Turkey and the capital of Trabzon Province. The city was founded in 756 BC as "Trapezous" by colonists from Miletus. It was added into the Achaemenid Em ...

Pentagon In geometry, a pentagon () is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is 540°. A pentagon may be simple or list of self-intersecting polygons, self-intersecting. A self-intersecting ...

– 5 sides *

Hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is de ...

– 6 sides ** Lemoine hexagon *

Heptagon In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using ''Wikt:septa-, septa-'' (an elision of ''Wikt:septua-, septua-''), a Latin-derived numerical prefix, rather than ...

– 7 sides *

Octagon In geometry, an octagon () is an eight-sided polygon or 8-gon. A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, which alternates two types of edges. A truncated octagon, t is a ...

– 8 sides *

Nonagon In geometry, a nonagon () or enneagon () is a nine-sided polygon or 9-gon. The name ''nonagon'' is a prefix Hybrid word, hybrid formation, from Latin (''nonus'', "ninth" + ''gonon''), used equivalently, attested already in the 16th century in Fre ...

– 9 sides *

Decagon In geometry, a decagon (from the Greek δέκα ''déka'' and γωνία ''gonía,'' "ten angles") is a ten-sided polygon or 10-gon.. The total sum of the interior angles of a simple decagon is 1440°. Regular decagon A '' regular decagon'' has a ...

– 10 sides * Hendecagon – 11 sides *

Dodecagon In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. Regular dodecagon A regular polygon, regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry ...

– 12 sides *

Tridecagon In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon. Regular tridecagon A ''regular polygon, regular tridecagon'' is represented by Schläfli symbol . The measure of each internal angle of a Regular polygon, regula ...

– 13 sides * Tetradecagon – 14 sides *

Pentadecagon In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon. Regular pentadecagon A '' regular pentadecagon'' is represented by Schläfli symbol . A regular pentadecagon has interior angles of 156 °, and with a side ...

– 15 sides *

Hexadecagon In mathematics, a hexadecagon (sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon. Regular hexadecagon A ''regular polygon, regular hexadecagon'' is a hexadecagon in which all angles are equal and all sides are congruent. It ...

– 16 sides *

Heptadecagon In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon. Regular heptadecagon A ''regular polygon, regular heptadecagon'' is represented by the Schläfli symbol . Construction As 17 is a Fermat prime, the regular he ...

– 17 sides *

Octadecagon In geometry, an octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon. Regular octadecagon A ''regular polygon, regular octadecagon'' has a Schläfli symbol and can be constructed as a quasiregular Truncation (geometry), trunc ...

– 18 sides * Enneadecagon – 19 sides *

Icosagon In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees. Regular icosagon The Regular polygon, regular icosagon has Schläfli symbol , and can also be constructed as a Truncation ( ...

– 20 sides * Icosikaihenagon - 21 sides * Icosikaidigon - 22 sides *

Icositrigon In geometry, an icositrigon (or icosikaitrigon) or 23-gon is a 23-sided polygon. The icositrigon has the distinction of being the smallest regular polygon that is not Neusis construction, neusis constructible. Regular icositrigon A ''regular pol ...

- 23 sides *

Icositetragon In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon. The sum of any icositetragon's interior angles is 3960 degrees. Regular icositetragon The ''regular polygon, regular icositetragon'' is represented by S ...

- 24 sides * Icosikaipentagon - 25 sides * Icosikaihexagon - 26 sides * Icosikaiheptagon - 27 sides * Icosikaioctagon - 28 sides * Icosikaienneagon - 29 sides *

Triacontagon In geometry, a triacontagon or 30-gon is a thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 (number), 5040 degrees. Regular triacontagon The ''regular polygon, regular triacontagon'' is a constructible polygon, by an ...

- 30 sides * Tetracontagon - 40 sides * Pentacontagon - 50 sides * Hexacontagon - 60 sides * Heptacontagon - 70 sides * Octacontagon - 80 sides * Enneacontagon - 90 sides * Hectogon - 100 sides * Dihectogon - 200 sides * Trihectogon - 300 sides * Tetrahectogon - 400 sides * Pentahectogon - 500 sides * Hexahectogon - 600 sides * Heptahectogon - 700 sides * Octahectogon - 800 sides * Enneahectogon - 900 sides * Chiliagon - 1,000 sides * Myriagon - 10,000 sides * Megagon - 1,000,000 sides *

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, Decagram (geometry)#Related figures, certain notable ones can ...

– there are multiple types of stars **

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 around ...

- star polygon with 5 sides **

Hexagram , can be seen as a compound polygon, 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 l ...

– star polygon with 6 sides ***

Star of David The Star of David (, , ) is a symbol generally recognized as representing both Jewish identity and Judaism. Its shape is that of a hexagram: the compound of two equilateral triangles. A derivation of the Seal of Solomon was used for decora ...

(example) **

Heptagram A heptagram, septagram, septegram or septogram is a seven-point star polygon, star drawn with seven straight strokes. The name ''heptagram'' combines a numeral prefix, ''hepta-'', with the Greek language, Greek suffix ''wikt:-gram, -gram ...

– star polygon with 7 sides **

Octagram In geometry, an octagram is an eight-angled star polygon. The name ''octagram'' combine a Greek numeral prefix, ''wikt:octa-, octa-'', with the Greek language, Greek suffix ''wikt:-gram, -gram''. The ''-gram'' suffix derives from γραμμή ...

– star polygon with 8 sides *** Star of Lakshmi (example) **

Enneagram Enneagram may refer to: * Enneagram (geometry), a nine-sided star polygon with various configurations * Enneagram of Personality, a model of human personality illustrated by an enneagram figure See also * Enneagon In geometry, a nonagon () or ...

- star polygon with 9 sides ** Decagram - star polygon with 10 sides **

Hendecagram In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven Vertex (geometry), vertices. The name ''hendecagram'' combines a Greek numeral prefix, ''wikt:hendeca-, hendeca-'', with the Greek language, Greek suffix ...

- star polygon with 11 sides **

Dodecagram In geometry, a dodecagram (γραμμή
Henry George Liddell, Robe ...

- star polygon with 12 sides *

Apeirogon In geometry, an apeirogon () or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case of infinite polytopes. In some literature, the term "apeirogon" may refer only to the regular apeirogon, with an in ...

- generalized polygon with countably infinite set of sides

Curved

Composed of circular arcs

* Annulus *

Arbelos In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that conta ...

Circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

** Archimedes' twin circles ** Bankoff circle ** Circular triangle *** Reuleaux triangle **

Circumcircle In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertex (geometry), vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumrad ...

** Disc **

Incircle and excircles of a triangle In geometry, the incircle or inscribed circle of a triangle is the largest circle that can be contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incente ...

Nine-point circle In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is so named because it passes through nine significant concyclic points defined from the triangle. These nine points are: * The midpoint of each s ...

Circular sector A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the ''minor ...

Circular segment In geometry, a circular segment or disk segment (symbol: ) is a region of a disk which is "cut off" from the rest of the disk by a straight line. The complete line is known as a '' secant'', and the section inside the disk as a '' chord''. More ...

Crescent A crescent shape (, ) is a symbol or emblem used to represent the lunar phase (as it appears in the northern hemisphere) in the first quarter (the "sickle moon"), or by extension a symbol representing the Moon itself. In Hindu iconography, Hind ...

Lens A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements'') ...

vesica piscis The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other. In Latin, "" literally means "bla ...

(fish bladder) *

Lune Lune may refer to: Rivers *River Lune, in Lancashire and Cumbria, England *River Lune, Durham, in County Durham, England *Lune (Weser), a 43 km-long tributary of the Weser in Germany *Lune River (Tasmania), in south-eastern Tasmania, Australia Pl ...

Quatrefoil A quatrefoil (anciently caterfoil) is a decorative element consisting of a symmetrical shape which forms the overall outline of four partially overlapping circles of the same diameter. It is found in art, architecture, heraldry and traditional ...

* Reuleaux polygon ** Reuleaux triangle * Salinon *

Semicircle In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, radians, or a half-turn). It only has one line of symmetr ...

Tomahawk A tomahawk is a type of single-handed axe used by the many Native Americans in the United States, Indian peoples and nations of North America, traditionally resembles a hatchet with a straight shaft. Etymology The name comes from Powhatan langu ...

Trefoil A trefoil () is a graphic form composed of the outline of three overlapping rings, used in architecture, Pagan and Christian symbolism, among other areas. The term is also applied to other symbols with a threefold shape. A similar shape with f ...

* Triquetra

Not composed of circular arcs

Archimedean spiral The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Ancient Greece, Greek mathematician Archimedes. The term ''Archimedean spiral'' is sometimes used to refer to the more gene ...

Astroid In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusp (singularity), cusps. Specifically, it is the Locus (mathematics), locus of a point on a circle as it Rolling, rolls inside a fixed circle with f ...

* Cardioid *

Deltoid Deltoid (delta-shaped) can refer to: * The deltoid muscle, a muscle in the shoulder * Kite (geometry), also known as a deltoid, a type of quadrilateral * A deltoid curve, a three-cusped hypocycloid * A leaf shape * The deltoid tuberosity, a part o ...

Ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...

* Various

lemniscate In algebraic geometry, a lemniscate ( or ) is any of several figure-eight or -shaped curves. The word comes from the Latin , meaning "decorated with ribbons", from the Greek (), meaning "ribbon",. or which alternatively may refer to the wool fr ...

s *

Oval An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas of mathematics (projective geometry, technical drawing, etc.), it is given a more precise definition, which may inc ...

** Cartesian oval ** Cassini oval ** Oval of Booth *

Superellipse A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but defined by an equation that allows ...

Taijitu In Chinese philosophy, a ''taijitu'' () is a Character (symbol), symbol or diagram () representing ''Taiji (philosophy), taiji'' () in both its monist (''Wuji (philosophy), wuji'') and its Dualism in cosmology, dualist (yin and yang) forms in a ...

* Tomoe *

Magatama are curved, comma-shaped beads that appeared in prehistoric Japan from the Jōmon period, Final Jōmon period through the Kofun period, approximately 1000 BCE to the 6th century CE. The beads, also described as jewels, were made of stone and e ...

References

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