List Of Mathematical Shapes

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From Wikipedia, the free encyclopedia
Following is a list of some mathematically well-defined shapes.
== Algebraic curves ==
Main article: List of curves
* Cubic plane curve
* Quartic plane curve
=== Rational curves ===
==== Degree 2 ====
* Conic sections
* Unit circle
* Unit hyperbola
==== Degree 3 ====
* Folium of Descartes
* Cissoid of Diocles
* Conchoid of de Sluze
* Right strophoid
* Semicubical parabola
* Serpentine curve
* Trident curve
* Trisectrix of Maclaurin
* Tschirnhausen cubic
* Witch of Agnesi
==== Degree 4 ====
* Ampersand curve
* Bean curve
* Bicorn
* Bow curve
* Bullet-nose curve
* Cruciform curve
* Deltoid curve
* Devil's curve
* Hippopede
* Kampyle of Eudoxus
* Kappa curve
* Lemniscate of Booth
* Lemniscate of Gerono
* Lemniscate of Bernoulli
* Limaçon
** Cardioid
** Limaçon trisectrix
* Trifolium curve[citation needed]
==== Degree 5 ====
* Quintic of l'Hospital
==== Degree 6 ====
* Astroid
* Atriphtaloid
* Nephroid
* Quadrifolium
==== Families of variable degree ====
* Epicycloid
* Epispiral
* Epitrochoid
* Hypocycloid
* Lissajous curve
* Poinsot's spirals
* Rational normal curve
* Rose curve
=== Curves of genus one ===
* Bicuspid curve
* Cassini oval
* Cassinoide
* Cubic curve
* Elliptic curve
* Watt's curve
=== Curves with genus greater than one ===
* Butterfly curve
* Elkies trinomial curves
* Hyperelliptic curve
* Klein quartic
* Classical modular curve
* Bolza surface
* Macbeath surface
=== Curve families with variable genus ===
* Polynomial lemniscate
* Fermat curve
* Sinusoidal spiral
* Superellipse
* Hurwitz surface
== Transcendental curves ==
* Bowditch curve
* Brachistochrone
* Butterfly curve
* Catenary
* Clélies
* Cochleoid
* Cycloid
* Horopter
* Isochrone
** Isochrone of Huygens (Tautochrone)
** Isochrone of Leibniz
** Isochrone of Varignon
* Lamé curve
* Pursuit curve
* Rhumb line
* Spirals
** Archimedean spiral
** Cornu spiral
** Cotes' spiral
** Fermat's spiral
** Galileo's spiral
** Hyperbolic spiral
** Lituus
** Logarithmic spiral
** Nielsen's spiral
* Syntractrix
* Tractrix
* Trochoid
== Piecewise constructions ==
* Bézier curve
* Splines
** B-spline
** Nonuniform rational B-spline
* Ogee
* Loess curve
* Lowess
* Polygonal curve
** Maurer rose
* Reuleaux triangle
* Bézier triangle
== Curves generated by other curves ==
* Caustic including Catacaustic and Diacaustic
* Cissoid
* Conchoid
* Evolute
* Glissette
* Inverse curve
* Involute
* Isoptic including Orthoptic
* Orthotomic
* Negative pedal curve
* Pedal curve
* Parallel curve
* Radial curve
* Roulette
* Strophoid
== Space curves ==
* Conchospiral
* Helix
** Tendril perversion (a transition between back-to-back helices)
** Hemihelix, a quasi-helical shape characterized by multiple tendril perversions
* Seiffert's spiral
* Slinky spiral
* Twisted cubic
* Viviani's curve
== Surfaces in 3-space ==
Main article: List of surfaces
* Plane
* Quadric surfaces
** Cone
** Cylinder
** Ellipsoid
*** Spheroid
**** Sphere
** Hyperboloid
** Paraboloid
* Bicylinder
* Tricylinder
* Möbius strip
* Torus
== Minimal surfaces ==
* Catalan's minimal surface
* Costa's minimal surface
* Catenoid
* Enneper surface
* Gyroid
* Helicoid
* Lidinoid
* Riemann's minimal surface
* Saddle tower
* Scherk surface
* Schwarz minimal surface
* Triply periodic minimal surface
== Non-orientable surfaces ==
* Klein bottle
* Real projective plane
** Cross-cap
** Roman surface
** Boy's surface
== Quadrics ==
* Sphere
* Spheroid
** Oblate spheroid
* Cone
* Ellipsoid
* Hyperboloid of one sheet
* Hyperboloid of two sheets
* Hyperbolic paraboloid (a ruled surface)
* Paraboloid
* Sphericon
* Oloid
== Pseudospherical surfaces ==
* Dini's surface
* Pseudosphere
== Algebraic surfaces ==
See the list of algebraic surfaces.
* Cayley cubic
* Barth sextic
* Clebsch cubic
* Monkey saddle (saddle-like surface for 3 legs.)
* Torus
* Dupin cyclide (inversion of a torus)
* Whitney umbrella
== Miscellaneous surfaces ==
* Right conoid (a ruled surface)
== Fractals ==
Main article: List of fractals by Hausdorff dimension
* Apollonian gasket
* Apollonian sphere packing
* Blancmange curve
* Cantor dust
* Cantor set
* Cantor tesseract[citation needed]
* Circle inversion fractal
* De Rham curve
* Douady rabbit
* Dragon curve
* Fibonacci word fractal
* Flame fractal
* Fractal curve
* Gosper curve
* Gosper island
* H-fractal
* Hénon map
* Hexaflake
* Hilbert curve
* Ikeda map attractor
* Iterated function system
* Jerusalem cube
* Julia set
* Koch curve
* Koch snowflake
* L-system
* Lévy C curve
* Feigenbaum attractor
* Lorenz attractor
* Lyapunov fractal
* Mandelbrot set
* Mandelbrot tree
* Mandelbulb
* Menger sponge
* Monkeys tree
* Moore curve
* N-flake
* Pascal triangle
* Peano curve
* Penrose tiling
* Pinwheel tiling
* Pythagoras tree
* Rauzy fractal
* Rössler attractor
* Sierpiński arrowhead curve
* Sierpinski carpet
* Sierpiński curve
* Sierpinski triangle
* Smith–Volterra–Cantor set
* T-square
* Takagi or Blancmange curve
* Triflake[citation needed]
* Vicsek fractal
* von Koch curve
* Weierstrass function
* Z-order curve
=== Random fractals ===
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* von Koch curve with random interval
* von Koch curve with random orientation
* polymer shapes
* diffusion-limited aggregation
* Self-avoiding random walk
* Brownian motion
* Lichtenberg figure
* Percolation theory
* Multiplicative cascade
== Regular polytopes ==
This table shows a summary of regular polytope counts by dimension.
Dimension	Convex 	Nonconvex 	Convex
Euclidean
tessellations	Convex
hyperbolic
tessellations	Nonconvex
hyperbolic
tessellations	Hyperbolic Tessellations
with infinite cells
and/or vertex figures	Abstract
Polytopes
1 	1 line segment 	0 	1 	0	0	0 	1
2 	∞ polygons 	∞ star polygons 	1 	1	0	0 	∞
3 	5 Platonic solids 	4 Kepler–Poinsot solids 	3 tilings 	∞	∞	∞ 	∞
4 	6 convex polychora 	10 Schläfli–Hess polychora	1 honeycomb 	4	0	11	∞
5 	3 convex 5-polytopes	0 	3 tetracombs	5	4	2 	∞
6 	3 convex 6-polytopes	0 	1 pentacombs	0	0	5 	∞
7+ 	3 	0 	1 	0	0	0 	∞
There are no nonconvex Euclidean regular tessellations in any number of dimensions.
=== Polytope elements ===
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
* Vertex, a 0-dimensional element
* Edge, a 1-dimensional element
* Face, a 2-dimensional element
* Cell, a 3-dimensional element
* Hypercell or Teron, a 4-dimensional element
* Facet, an (n-1)-dimensional element
* Ridge, an (n-2)-dimensional element
* Peak, an (n-3)-dimensional element
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak.
* Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
=== Tessellations ===
The classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
=== Zero dimension ===
* Point
=== One-dimensional regular polytope ===
There is only one polytope in 1 dimension, whose boundaries are the two endpoints of a line segment, represented by the empty Schläfli symbol {}.
=== Two-dimensional regular polytopes ===
* Polygon
* Equilateral
* Cyclic polygon
* Convex polygon
* Star polygon
* Pentagram
==== Convex ====
* Regular polygon
* Equilateral triangle
* Simplex
* Square
* Cross-polytope
* Hypercube
* Pentagon
* Hexagon
* Heptagon
* Octagon
* Enneagon
* Decagon
* Hendecagon
* Dodecagon
* Tridecagon
* Tetradecagon
* Pentadecagon
* Hexadecagon
* Heptadecagon
* Octadecagon
* Enneadecagon
* Icosagon
* Hectogon
* Chiliagon
* Regular polygon
===== Degenerate (spherical) =====
* Monogon
* Digon
==== Non-convex ====
* star polygon
* Pentagram
* Heptagram
* Octagram
* Enneagram
* Decagram
==== Tessellation ====
* Apeirogon
=== Three-dimensional regular polytopes ===
* polyhedron
==== Convex ====
* Platonic solid
** Tetrahedron, the 3-space Simplex
** Cube, the 3-space hypercube
** Octahedron, the 3-space Cross-polytope
** Dodecahedron
** Icosahedron
==== Degenerate (spherical) ====
* hosohedron
* dihedron
* Henagon#In spherical geometry
==== Non-convex ====
* Kepler–Poinsot polyhedra
** Small stellated dodecahedron
** Great dodecahedron
** Great stellated dodecahedron
** Great icosahedron
==== Tessellations ====
===== Euclidean tilings =====
* Square tiling
* Triangular tiling
* Hexagonal tiling
* Apeirogon
* Dihedron
===== Hyperbolic tilings =====
* Lobachevski plane
* Hyperbolic tiling
===== Hyperbolic star-tilings =====
* Order-7 heptagrammic tiling
* Heptagrammic-order heptagonal tiling
* Order-9 enneagrammic tiling[citation needed]
* Enneagrammic-order enneagonal tiling[citation needed]
=== Four-dimensional regular polytopes ===
* convex regular 4-polytope
** 5-cell, the 4-space Simplex
** 8-cell, the 4-space Hypercube
** 16-cell, the 4-space Cross-polytope
** 24-cell
** 120-cell
** 600-cell
==== Degenerate (spherical) ====
* Ditope
* Hosotope
* 3-sphere
==== Non-convex ====
* Star or (Schläfli–Hess) regular 4-polytope
** Icosahedral 120-cell
** Small stellated 120-cell
** Great 120-cell
** Grand 120-cell
** Great stellated 120-cell
** Grand stellated 120-cell
** Great grand 120-cell
** Great icosahedral 120-cell
** Grand 600-cell
** Great grand stellated 120-cell
==== Tessellations of Euclidean 3-space ====
* Honeycomb
* Cubic honeycomb
==== Degenerate tessellations of Euclidean 3-space ====
* Hosohedron
* Dihedron
* Order-2 apeirogonal tiling
* Apeirogonal hosohedron
* Order-4 square hosohedral honeycomb
* Order-6 triangular hosohedral honeycomb
* Hexagonal hosohedral honeycomb[citation needed]
* Order-2 square tiling honeycomb
* Order-2 triangular tiling honeycomb
* Order-2 hexagonal tiling honeycomb
==== Tessellations of hyperbolic 3-space ====
* Order-4 dodecahedral honeycomb
* Order-5 dodecahedral honeycomb
* Order-5 cubic honeycomb
* Icosahedral honeycomb
* Order-3 icosahedral honeycomb
* Order-4 octahedral honeycomb
* Triangular tiling honeycomb
* Square tiling honeycomb
* Order-4 square tiling honeycomb
* Order-6 tetrahedral honeycomb
* Order-6 cubic honeycomb
* Order-6 dodecahedral honeycomb
* Hexagonal tiling honeycomb
* Order-4 hexagonal tiling honeycomb
* Order-5 hexagonal tiling honeycomb
* Order-6 hexagonal tiling honeycomb
=== Five-dimensional regular polytopes and higher ===
* 5-polytope
* Honeycomb
* Tetracomb
Simplex 	Hypercube	Cross-polytope
5-simplex 	5-cube 	5-orthoplex
6-simplex 	6-cube 	6-orthoplex
7-simplex 	7-cube 	7-orthoplex
8-simplex 	8-cube 	8-orthoplex
9-simplex 	9-cube 	9-orthoplex
10-simplex	10-cube 	10-orthoplex
11-simplex	11-cube 	11-orthoplex
==== Tessellations of Euclidean 4-space ====
* honeycombs
* Tesseractic honeycomb
* 16-cell honeycomb
* 24-cell honeycomb
==== Tessellations of Euclidean 5-space and higher ====
* Hypercubic honeycomb
* Hypercube
* Square tiling
* Cubic honeycomb
* Tesseractic honeycomb
* 5-cube honeycomb
* 6-cube honeycomb
* 7-cube honeycomb
* 8-cube honeycomb
* Hypercubic honeycomb
==== Tessellations of hyperbolic 4-space ====
* honeycombs
* Order-5 5-cell honeycomb
* 120-cell honeycomb
* Order-5 tesseractic honeycomb
* Order-4 120-cell honeycomb
* Order-5 120-cell honeycomb
* Order-4 24-cell honeycomb
* Cubic honeycomb honeycomb
* Small stellated 120-cell honeycomb
* Pentagrammic-order 600-cell honeycomb
* Order-5 icosahedral 120-cell honeycomb
* Great 120-cell honeycomb
==== Tessellations of hyperbolic 5-space ====
* 5-orthoplex honeycomb
* 24-cell honeycomb honeycomb
* 16-cell honeycomb honeycomb
* Order-4 24-cell honeycomb honeycomb
* Tesseractic honeycomb honeycomb
=== Apeirotopes ===
* Apeirotope
** Apeirogon
** Apeirohedron
** Regular skew polyhedron
=== Abstract polytopes ===
* Abstract polytope
** 11-cell
** 57-cell
== 2D with 1D surface ==
* Convex polygon
* Concave polygon
* Constructible polygon
* Cyclic polygon
* Equiangular polygon
* Equilateral polygon
* Regular polygon
* Penrose tile
* Polyform
* Balbis
* Gnomon
* Golygon
* Star without crossing lines
* Star polygon
** Hexagram
*** Star of David
** Heptagram
** Octagram
*** Star of Lakshmi
** Decagram
** Pentagram
Polygons named for their number of sides
* Monogon — 1 sided
* Digon — 2 sided
* Triangle
** Acute triangle
** Equilateral triangle
** Isosceles triangle
** Obtuse triangle
** Rational triangle
** Right triangle
*** 30-60-90 triangle
*** Isosceles right triangle
*** Kepler triangle
** Scalene triangle
* Quadrilateral
** Cyclic quadrilateral
*** square
** kite
** Parallelogram
*** Rhombus (equilateral parallelogram)
**** Lozenge
*** Rhomboid
*** Rectangle
**** square (regular quadrilateral)
** Tangential quadrilateral
** Trapezoid or trapezium
*** Isosceles trapezoid
* Pentagon
** Regular pentagon
* Hexagon
** Lemoine hexagon
* Heptagon
* Octagon
** Regular octagon
* Nonagon
* Decagon
** Regular decagon
* Hendecagon
* Dodecagon
* Triskaidecagon
* Tetradecagon
* Pentadecagon
* Hexadecagon
* Heptadecagon
* Octadecagon
* Enneadecagon
* Icosagon
* Triacontagon
* Tetracontagon
* Pentacontagon
* Hexacontagon
* Heptacontagon
* Octacontagon
* Enneacontagon
* Hectogon
* 257-gon
* Chiliagon
* Myriagon
* 65537-gon
* Megagon
* Apeirogon
=== Tilings ===
* List of uniform tilings
* Uniform tilings in hyperbolic plane
* Archimedean tiling
** Square tiling
** Triangular tiling
** Hexagonal tiling
** Truncated square tiling
** Snub square tiling
** Trihexagonal tiling
** Truncated hexagonal tiling
** Rhombitrihexagonal tiling
** Truncated trihexagonal tiling
** Snub hexagonal tiling
** Elongated triangular tiling
=== Uniform polyhedra ===
Main article: Uniform polyhedron
* Regular polyhedron
** Platonic solid
*** Tetrahedron
*** Cube
*** Octahedron
*** Dodecahedron
*** Icosahedron
** Kepler–Poinsot polyhedron (regular star polyhedra)
*** Great icosahedron
*** Small stellated dodecahedron
*** Great dodecahedron
*** Great stellated dodecahedron
** Abstract regular polyhedra (Projective polyhedron)
*** Hemicube
*** Hemi-octahedron
*** Hemi-dodecahedron
*** Hemi-icosahedron
* Archimedean solid
** Truncated tetrahedron
** Cuboctahedron
** Truncated cube
** Truncated octahedron
** Rhombicuboctahedron
** Truncated cuboctahedron
** Snub cube
** Icosidodecahedron
** Truncated dodecahedron
** Truncated icosahedron
** Rhombicosidodecahedron
** Truncated icosidodecahedron
** Snub dodecahedron
* Prismatic uniform polyhedron
** Prism
** Antiprism
* Uniform star polyhedron
** Cubitruncated cuboctahedron
** Cubohemioctahedron
** Ditrigonal dodecadodecahedron
** Dodecadodecahedron
** Great cubicuboctahedron
** Great dirhombicosidodecahedron
** Great disnub dirhombidodecahedron
** Great ditrigonal dodecicosidodecahedron
** Great ditrigonal icosidodecahedron
** Great dodecahemicosahedron
** Great dodecahemidodecahedron
** Great dodecicosahedron
** Great dodecicosidodecahedron
** Great icosicosidodecahedron
** Great icosidodecahedron
** Great icosihemidodecahedron
** Great inverted snub icosidodecahedron
** Great retrosnub icosidodecahedron
** Great rhombidodecahedron
** Great rhombihexahedron
** Great snub dodecicosidodecahedron
** Great snub icosidodecahedron
** Great stellated truncated dodecahedron
** Great truncated cuboctahedron
** Great truncated icosidodecahedron
** Icosidodecadodecahedron
** Icositruncated dodecadodecahedron
** Inverted snub dodecadodecahedron
** Nonconvex great rhombicosidodecahedron
** Nonconvex great rhombicuboctahedron
** Octahemioctahedron
** Rhombicosahedron
** Rhombidodecadodecahedron
** Small cubicuboctahedron
** Small ditrigonal dodecicosidodecahedron
** Small ditrigonal icosidodecahedron
** Small dodecahemicosahedron
** Small dodecahemidodecahedron
** Small dodecicosahedron
** Small dodecicosidodecahedron
** Small icosicosidodecahedron
** Small icosihemidodecahedron
** Small retrosnub icosicosidodecahedron
** Small rhombidodecahedron
** Small rhombihexahedron
** Small snub icosicosidodecahedron
** Small stellated truncated dodecahedron
** Snub dodecadodecahedron
** Snub icosidodecadodecahedron
** Stellated truncated hexahedron
** Tetrahemihexahedron
** Truncated dodecadodecahedron
** Truncated great dodecahedron
** Truncated great icosahedron
=== Duals of uniform polyhedra ===
* Catalan solid
** Triakis tetrahedron
** Rhombic dodecahedron
** Triakis octahedron
** Tetrakis hexahedron
** Deltoidal icositetrahedron
** Disdyakis dodecahedron
** Pentagonal icositetrahedron
** Rhombic triacontahedron
** Triakis icosahedron
** Pentakis dodecahedron
** Deltoidal hexecontahedron
** Disdyakis triacontahedron
** Pentagonal hexecontahedron
* non-convex
** Great complex icosidodecahedron
** Great deltoidal hexecontahedron
** Great deltoidal icositetrahedron
** Great dirhombicosidodecacron
** Great dirhombicosidodecahedron
** Great disdyakis dodecahedron
** Great disdyakis triacontahedron
** Great disnub dirhombidodecacron
** Great ditrigonal dodecacronic hexecontahedron
** Great dodecacronic hexecontahedron
** Great dodecahemicosacron
** Great dodecicosacron
** Great hexacronic icositetrahedron
** Great hexagonal hexecontahedron
** Great icosacronic hexecontahedron
** Great icosihemidodecacron
** Great inverted pentagonal hexecontahedron
** Great pentagonal hexecontahedron
** Great pentagrammic hexecontahedron
** Great pentakis dodecahedron
** Great rhombic triacontahedron
** Great rhombidodecacron
** Great rhombihexacron
** Great stellapentakis dodecahedron
** Great triakis icosahedron
** Great triakis octahedron
** Great triambic icosahedron
** Medial deltoidal hexecontahedron
** Medial disdyakis triacontahedron
** Medial hexagonal hexecontahedron
** Medial icosacronic hexecontahedron
** Medial inverted pentagonal hexecontahedron
** Medial pentagonal hexecontahedron
** Medial rhombic triacontahedron
** Hexahemioctacron
** Hemipolyhedron
** Octahemioctacron
** Rhombicosacron
** Small complex icosidodecahedron
** Small ditrigonal dodecacronic hexecontahedron
** Small dodecacronic hexecontahedron
** Small dodecahemicosacron
** Small dodecahemidodecacron
** Small dodecicosacron
** Small hexacronic icositetrahedron
** Small hexagonal hexecontahedron
** Small hexagrammic hexecontahedron
** Small icosacronic hexecontahedron
** Small icosihemidodecacron
** Small rhombidodecacron
** Small rhombihexacron
** Small stellapentakis dodecahedron
** Small triambic icosahedron
** Tetrahemihexacron
=== Johnson solids ===
Main article: Johnson solid
* Augmented dodecahedron
* Augmented hexagonal prism
* Augmented pentagonal prism
* Augmented sphenocorona
* Augmented triangular prism
* Augmented tridiminished icosahedron
* Augmented truncated cube
* Augmented truncated dodecahedron
* Augmented truncated tetrahedron
* Biaugmented pentagonal prism
* Biaugmented triangular prism
* Biaugmented truncated cube
* Bigyrate diminished rhombicosidodecahedron
* Bilunabirotunda
* Diminished rhombicosidodecahedron
* Disphenocingulum
* Elongated pentagonal bipyramid
* Elongated pentagonal cupola
* Elongated pentagonal gyrobicupola
* Elongated pentagonal gyrobirotunda
* Elongated pentagonal gyrocupolarotunda
* Elongated pentagonal orthobicupola
* Elongated pentagonal orthobirotunda
* Elongated pentagonal orthocupolarotunda
* Elongated pentagonal pyramid
* Elongated pentagonal rotunda
* Elongated square bipyramid
* Elongated square cupola
* Elongated square gyrobicupola
* Elongated square pyramid
* Elongated triangular bipyramid
* Elongated triangular cupola
* Elongated triangular gyrobicupola
* Elongated triangular orthobicupola
* Elongated triangular pyramid
* Gyrate bidiminished rhombicosidodecahedron
* Gyrate rhombicosidodecahedron
* Gyrobifastigium
* Gyroelongated pentagonal bicupola
* Gyroelongated pentagonal birotunda
* Gyroelongated pentagonal cupola
* Gyroelongated pentagonal cupolarotunda
* Gyroelongated pentagonal pyramid
* Gyroelongated pentagonal rotunda
* Gyroelongated square bicupola
* Gyroelongated square bipyramid
* Gyroelongated square cupola
* Gyroelongated square pyramid
* Gyroelongated triangular bicupola
* Gyroelongated triangular cupola
* Hebesphenomegacorona
* Metabiaugmented dodecahedron
* Metabiaugmented hexagonal prism
* Metabiaugmented truncated dodecahedron
* Metabidiminished icosahedron
* Metabidiminished rhombicosidodecahedron
* Metabigyrate rhombicosidodecahedron
* Metagyrate diminished rhombicosidodecahedron
* Parabiaugmented dodecahedron
* Parabiaugmented hexagonal prism
* Parabiaugmented truncated dodecahedron
* Parabidiminished rhombicosidodecahedron
* Parabigyrate rhombicosidodecahedron
* Paragyrate diminished rhombicosidodecahedron
* Pentagonal bipyramid
* Pentagonal cupola
* Pentagonal gyrobicupola
* Pentagonal gyrocupolarotunda
* Pentagonal orthobicupola
* Pentagonal orthobirotunda
* Pentagonal orthocupolarotunda
* Pentagonal pyramid
* Pentagonal rotunda
* Snub disphenoid
* Snub square antiprism
* Sphenocorona
* Sphenomegacorona
* Square cupola
* Square gyrobicupola
* Square orthobicupola
* Square pyramid
* Triangular bipyramid
* Triangular cupola
* Triangular hebesphenorotunda
* Triangular orthobicupola
* Triaugmented dodecahedron
* Triaugmented hexagonal prism
* Triaugmented triangular prism
* Triaugmented truncated dodecahedron
* Tridiminished icosahedron
* Tridiminished rhombicosidodecahedron
* Trigyrate rhombicosidodecahedron
=== Other nonuniform polyhedra ===
* Pyramid
* Bipyramid
* Disphenoid
* Parallelepiped
* Cuboid
* Rhombohedron
* Trapezohedron
* Frustum
* Trapezo-rhombic dodecahedron
* Rhombo-hexagonal dodecahedron
* Truncated trapezohedron
* Deltahedron
* Zonohedron
* Prismatoid
* Cupola
* Bicupola
=== Spherical polyhedra ===
Main article: spherical polyhedron
* Dihedron
* Hosohedron
=== Honeycombs ===
; Convex uniform honeycomb
* Cubic honeycomb
* Truncated cubic honeycomb
* Bitruncated cubic honeycomb
* Cantellated cubic honeycomb
* Cantitruncated cubic honeycomb
* Rectified cubic honeycomb
* Runcitruncated cubic honeycomb
* Omnitruncated cubic honeycomb
* Tetrahedral-octahedral honeycomb
* Truncated alternated cubic honeycomb
* Cantitruncated alternated cubic honeycomb
* Runcinated alternated cubic honeycomb
* Quarter cubic honeycomb
* Gyrated tetrahedral-octahedral honeycomb
* Gyrated triangular prismatic honeycomb
* Gyroelongated alternated cubic honeycomb
* Gyroelongated triangular prismatic honeycomb
* Elongated triangular prismatic honeycomb
* Elongated alternated cubic honeycomb
* Hexagonal prismatic honeycomb
* Triangular prismatic honeycomb
* Triangular-hexagonal prismatic honeycomb
* Truncated hexagonal prismatic honeycomb
* Truncated square prismatic honeycomb
* Rhombitriangular-hexagonal prismatic honeycomb
* Omnitruncated triangular-hexagonal prismatic honeycomb
* Snub triangular-hexagonal prismatic honeycomb
* Snub square prismatic honeycomb
; Dual uniform honeycomb
* Disphenoid tetrahedral honeycomb
* Rhombic dodecahedral honeycomb
; Others
* Trapezo-rhombic dodecahedral honeycomb
* Weaire–Phelan structure
; Convex uniform honeycombs in hyperbolic space
* Order-4 dodecahedral honeycomb
* Order-5 cubic honeycomb
* Order-5 dodecahedral honeycomb
* Icosahedral honeycomb
=== Other ===
* Apeirogonal prism
* Apeirohedron
* Bicupola
* Cupola
* Bifrustum
* Boerdijk–Coxeter helix
* Császár polyhedron
* Flexible polyhedron
* Gyroelongated square dipyramid
* Heronian tetrahedron
* Hexagonal bifrustum
* Hexagonal truncated trapezohedron
* Hill tetrahedron
* Holyhedron
* Infinite skew polyhedron
* Jessen's icosahedron
* Near-miss Johnson solid
* Parallelepiped
* Pentagonal bifrustum
* Polytetrahedron
* Pyritohedron
* Rhombic enneacontahedron
* Rhombic icosahedron
* Rhombo-hexagonal dodecahedron
* Rhombohedron
* Scalenohedron
* Schönhardt polyhedron
* Square bifrustum
* Square truncated trapezohedron
* Szilassi polyhedron
* Tetradecahedron
* Tetradyakis hexahedron
* Tetrated dodecahedron
* Triangular bifrustum
* Triaugmented triangular prism
* Truncated rhombic dodecahedron
* Truncated trapezohedron
* Truncated triakis tetrahedron
* Tridyakis icosahedron
* Trigonal trapezohedron
* Regular skew polyhedron
* Waterman polyhedron
* Wedge
=== Regular and uniform compound polyhedra ===
; Polyhedral compound and Uniform polyhedron compound
* Compound of cube and octahedron
* Compound of dodecahedron and icosahedron
* Compound of eight octahedra with rotational freedom
* Compound of eight triangular prisms
* Compound of five cubes
* Compound of five cuboctahedra
* Compound of five cubohemioctahedra
* Compound of five great cubicuboctahedra
* Compound of five great dodecahedra
* Compound of five great icosahedra
* Compound of five great rhombihexahedra
* Compound of five icosahedra
* Compound of five octahedra
* Compound of five octahemioctahedra
* Compound of five small cubicuboctahedra
* Compound of five small rhombicuboctahedra
* Compound of five small rhombihexahedra
* Compound of five small stellated dodecahedra
* Compound of five stellated truncated cubes
* Compound of five tetrahedra
* Compound of five tetrahemihexahedra
* Compound of five truncated cubes
* Compound of five truncated tetrahedra
* Compound of five uniform great rhombicuboctahedra
* Compound of four hexagonal prisms
* Compound of four octahedra
* Compound of four octahedra with rotational freedom
* Compound of four tetrahedra
* Compound of four triangular prisms
* Compound of great icosahedron and great stellated dodecahedron
* Compound of six cubes with rotational freedom
* Compound of six decagonal prisms
* Compound of six decagrammic prisms
* Compound of six pentagonal prisms
* Compound of six pentagrammic crossed antiprisms
* Compound of six pentagrammic prisms
* Compound of six tetrahedra
* Compound of six tetrahedra with rotational freedom
* Compound of small stellated dodecahedron and great dodecahedron
* Compound of ten hexagonal prisms
* Compound of ten octahedra
* Compound of ten tetrahedra
* Compound of ten triangular prisms
* Compound of ten truncated tetrahedra
* Compound of three cubes
* Compound of three tetrahedra
* Compound of twelve pentagonal antiprisms with rotational freedom
* Compound of twelve pentagonal prisms
* Compound of twelve pentagrammic prisms
* Compound of twelve tetrahedra with rotational freedom
* Compound of twenty octahedra
* Compound of twenty octahedra with rotational freedom
* Compound of twenty tetrahemihexahedra
* Compound of twenty triangular prisms
* Compound of two great dodecahedra
* Compound of two great icosahedra
* Compound of two great inverted snub icosidodecahedra
* Compound of two great retrosnub icosidodecahedra
* Compound of two great snub icosidodecahedra
* Compound of two icosahedra
* Compound of two inverted snub dodecadodecahedra
* Compound of two small stellated dodecahedra
* Compound of two snub cubes
* Compound of two snub dodecadodecahedra
* Compound of two snub dodecahedra
* Compound of two snub icosidodecadodecahedra
* Compound of two truncated tetrahedra
* Prismatic compound of antiprisms
* Prismatic compound of antiprisms with rotational freedom
* Prismatic compound of prisms
* Prismatic compound of prisms with rotational freedom
* 4-polytope
** Hecatonicosachoron
** Hexacosichoron
** Hexadecachoron
** Icositetrachoron
** Pentachoron
** Tesseract
* Hypercone
; Convex regular 4-polytope
* 5-cell, Tesseract, 16-cell, 24-cell, 120-cell, 600-cell
; Abstract regular polytope
* 11-cell, 57-cell
; Schläfli–Hess 4-polytope (Regular star 4-polytope)
* Icosahedral 120-cell, Small stellated 120-cell, Great 120-cell, Grand 120-cell, Great stellated 120-cell, Grand stellated 120-cell, Great grand 120-cell, Great icosahedral 120-cell, Grand 600-cell, Great grand stellated 120-cell
; Uniform 4-polytope
* Rectified 5-cell, Truncated 5-cell, Cantellated 5-cell, Runcinated 5-cell
* Rectified tesseract, Truncated tesseract, Cantellated tesseract, Runcinated tesseract
* Rectified 16-cell, Truncated 16-cell
* Rectified 24-cell, Truncated 24-cell, Cantellated 24-cell, Runcinated 24-cell, Snub 24-cell
* Rectified 120-cell, Truncated 120-cell, Cantellated 120-cell, Runcinated 120-cell
* Rectified 600-cell, Truncated 600-cell, Cantellated 600-cell
; Prismatic uniform polychoron
* Grand antiprism
* Duoprism
* Tetrahedral prism, Truncated tetrahedral prism
* Truncated cubic prism, Truncated octahedral prism, Cuboctahedral prism, Rhombicuboctahedral prism, Truncated cuboctahedral prism, Snub cubic prism
* Truncated dodecahedral prism, Truncated icosahedral prism, Icosidodecahedral prism, Rhombicosidodecahedral prism, Truncated icosidodecahedral prism, Snub dodecahedral prism
* Uniform antiprismatic prism
=== Honeycombs ===
* Tesseractic honeycomb
* 24-cell honeycomb
* Snub 24-cell honeycomb
* Rectified 24-cell honeycomb
* Truncated 24-cell honeycomb
* 16-cell honeycomb
* 5-cell honeycomb
* Omnitruncated 5-cell honeycomb
* Truncated 5-cell honeycomb
* Omnitruncated 5-simplex honeycomb
== 5D with 4D surfaces ==
* regular 5-polytope
** 5-dimensional cross-polytope
** 5-dimensional hypercube
** 5-dimensional simplex
; Five-dimensional space, 5-polytope and uniform 5-polytope
* 5-simplex, Rectified 5-simplex, Truncated 5-simplex, Cantellated 5-simplex, Runcinated 5-simplex, Stericated 5-simplex
* 5-demicube, Truncated 5-demicube, Cantellated 5-demicube, Runcinated 5-demicube
* 5-cube, Rectified 5-cube, 5-cube, Truncated 5-cube, Cantellated 5-cube, Runcinated 5-cube, Stericated 5-cube
* 5-orthoplex, Rectified 5-orthoplex, Truncated 5-orthoplex, Cantellated 5-orthoplex, Runcinated 5-orthoplex
; Prismatic uniform 5-polytope
: For each polytope of dimension n, there is a prism of dimension n+1.[citation needed]
=== Honeycombs ===
* 5-cubic honeycomb
* 5-simplex honeycomb
* Truncated 5-simplex honeycomb
* 5-demicubic honeycomb
== Six dimensions ==
; Six-dimensional space, 6-polytope and uniform 6-polytope
* 6-simplex, Rectified 6-simplex, Truncated 6-simplex, Cantellated 6-simplex, Runcinated 6-simplex, Stericated 6-simplex, Pentellated 6-simplex
* 6-demicube, Truncated 6-demicube, Cantellated 6-demicube, Runcinated 6-demicube, Stericated 6-demicube
* 6-cube, Rectified 6-cube, 6-cube, Truncated 6-cube, Cantellated 6-cube, Runcinated 6-cube, Stericated 6-cube, Pentellated 6-cube
* 6-orthoplex, Rectified 6-orthoplex, Truncated 6-orthoplex, Cantellated 6-orthoplex, Runcinated 6-orthoplex, Stericated 6-orthoplex
* 122 polytope, 221 polytope
=== Honeycombs ===
* 6-cubic honeycomb
* 6-simplex honeycomb
* 6-demicubic honeycomb
* 222 honeycomb
== Seven dimensions ==
; Seven-dimensional space, uniform 7-polytope
* 7-simplex, Rectified 7-simplex, Truncated 7-simplex, Cantellated 7-simplex, Runcinated 7-simplex, Stericated 7-simplex, Pentellated 7-simplex, Hexicated 7-simplex
* 7-demicube, Truncated 7-demicube, Cantellated 7-demicube, Runcinated 7-demicube, Stericated 7-demicube, Pentellated 7-demicube
* 7-cube, Rectified 7-cube, 7-cube, Truncated 7-cube, Cantellated 7-cube, Runcinated 7-cube, Stericated 7-cube, Pentellated 7-cube, Hexicated 7-cube
* 7-orthoplex, Rectified 7-orthoplex, Truncated 7-orthoplex, Cantellated 7-orthoplex, Runcinated 7-orthoplex, Stericated 7-orthoplex, Pentellated 7-orthoplex
* 132 polytope, 231 polytope, 321 polytope
=== Honeycombs ===
* 7-cubic honeycomb
* 7-demicubic honeycomb
* 331 honeycomb, 133 honeycomb
== Eight dimension ==
; Eight-dimensional space, uniform 8-polytope
* 8-simplex, Rectified 8-simplex, Truncated 8-simplex, Cantellated 8-simplex, Runcinated 8-simplex, Stericated 8-simplex, Pentellated 8-simplex, Hexicated 8-simplex, Heptellated 8-simplex
* 8-orthoplex, Rectified 8-orthoplex, Truncated 8-orthoplex, Cantellated 8-orthoplex, Runcinated 8-orthoplex, Stericated 8-orthoplex, Pentellated 8-orthoplex, Hexicated 8-orthoplex[citation needed]
* 8-cube, Rectified 8-cube, Truncated 8-cube, Cantellated 8-cube, Runcinated 8-cube, Stericated 8-cube, Pentellated 8-cube, Hexicated 8-cube, Heptellated 8-cube[citation needed]
* 8-demicube, Truncated 8-demicube, Cantellated 8-demicube, Runcinated 8-demicube, Stericated 8-demicube, Pentellated 8-demicube, Hexicated 8-demicube[citation needed]
* 142 polytope, 241 polytope, 421 polytope, Truncated 421 polytope, Truncated 241 polytope, Truncated 142 polytope, Cantellated 421 polytope, Cantellated 241 polytope, Runcinated 421 polytope[citation needed]
=== Honeycombs ===
* 8-cubic honeycomb
* 8-demicubic honeycomb
* 521 honeycomb, 251 honeycomb, 152 honeycomb
== Nine dimensions ==
; 9-polytope
* 9-cube
* 9-demicube
* 9-orthoplex
* 9-simplex
=== Hyperbolic honeycombs ===
* E9 honeycomb
== Ten dimensions ==
; 10-polytope
* 10-cube
* 10-demicube
* 10-orthoplex
* 10-simplex
== Dimensional families ==
; Regular polytope and List of regular polytopes
* Simplex
* Hypercube
* Cross-polytope
; Uniform polytope
* Demihypercube
* Uniform 1k2 polytope
* Uniform 2k1 polytope
* Uniform k21 polytope
; Honeycombs
* Hypercubic honeycomb
* Alternated hypercubic honeycomb
== Geometry ==
* Triangle
* Automedian triangle
* Delaunay triangulation
* Equilateral triangle
* Golden triangle
* Hyperbolic triangle (non-Euclidean geometry)
* Isosceles triangle
* Kepler triangle
* Reuleaux triangle
* Right triangle
* Sierpinski triangle (fractal geometry)
* Special right triangles
* Spiral of Theodorus
* Thomson cubic
* Triangular bipyramid
* Triangular prism
* Triangular pyramid
* Triangular tiling
== Hyperplexicons ==
* Glowvoid
* Warith's void
* Warith's hyperplexicon shape
* Gaxxoid
* Gyroid
* Hyperplexicon Gyroid
* Planetium
* Epyoid
* Xenroid
* Xenoshape
* Xenoid
* Emperoids
** Hypervoid
** Hyperoid
** Warith-Nathaniyal mixbox
** Mixbox
** Forcoid
* Corporoid
* Primoid
* Oppan's gyroid
* Zahian's Hyperplexicon
* Nathaniyal's object
* Hyperplexicon
== Geometry and other areas of mathematics ==
link=https://en.wikipedia.org/wiki/File:Ford_circles.svg|right|thumb|350x350px|Ford circles
* Annulus
* Apollonian circles
* Apollonian gasket
* Arbelos
* Borromean rings
* Circle
* Circular sector
* Circular segment
* Cyclic quadrilateral
* Cycloid
* Epitrochoid
** Epicycloid
*** Cardioid
*** Nephroid
*** Deferent and epicycle
* Ex-tangential quadrilateral
* Horocycle
* Hypotrochoid
** Hypocycloid
*** Astroid
*** Deltoid curve
* Lune
* Pappus chain
* Peaucellier–Lipkin linkage
* Robbins pentagon
* Salinon
* Semicircle
* Squircle
* Steiner chain
* Tangential quadrilateral
** Bicentric quadrilateral
== Glyphs and symbols ==
* Borromean rings
* Crescent
* Vesica piscis
* Arc
* Caustic
* Cissoid
* Conchoid
* Cubic Hermite curve
* Curve of constant width
* hedgehog
* Parametric curve
** Bézier curve
** Spline
*** Hermite spline
**** Beta spline[citation needed]
***** B-spline
*** Higher-order spline[citation needed]
*** NURBS
* Ray
* Reuleaux triangle
* Ribaucour curve
== Table of all the Shapes ==
This is a table of all the shapes above.
Table of Shapes
Section 	Sub-Section 	Sup-Section	Name
Algebraic Curves	¿ Curves 	¿ Curves 	Cubic Plane Curve
Algebraic Curves	¿ Curves 	¿ Curves 	Quartic Plane Curve
Algebraic Curves	Rational Curves	Degree 2 	Conic Section(s)
Algebraic Curves	Rational Curves	Degree 2 	Unit Circle
Algebraic Curves	Rational Curves	Degree 2 	Unit Hyperbola
Algebraic Curves	Rational Curves	Degree 3 	Folium of Descartes
Algebraic Curves	Rational Curves	Degree 3 	Cissoid of Diocles
Algebraic Curves	Rational Curves	Degree 3 	Conchoid of de Sluze
Algebraic Curves	Rational Curves	Degree 3 	Right Strophoid
Algebraic Curves	Rational Curves	Degree 3 	Semicubical Parabola
Algebraic Curves	Rational Curves	Degree 3 	Serpentine Curve
Algebraic Curves	Rational Curves	Degree 3 	Trident Curve
Algebraic Curves	Rational Curves	Degree 3 	Trisectrix of Maclaurin
Algebraic Curves	Rational Curves	Degree 3 	Tschirnhausen Cubic
Algebraic Curves	Rational Curves	Degree 3 	Witch of Agnesi
Algebraic Curves	Rational Curves	Degree 4 	Ampersand Curve
Algebraic Curves	Rational Curves	Degree 4 	Bean Curve
Algebraic Curves	Rational Curves	Degree 4 	Bicorn
Algebraic Curves	Rational Curves	Degree 4 	Bow Curve
Algebraic Curves	Rational Curves	Degree 4 	Bullet-Nose Curve
Algebraic Curves	Rational Curves	Degree 4 	Cruciform Curve
Algebraic Curves	Rational Curves	Degree 4 	
Algebraic Curves	Rational Curves	Degree 4 	
Algebraic Curves	Rational Curves	Degree 4 	
== References ==
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Category: 
* Lists of shapes
* This page was last edited on 7 May 2024, at 22:16 (UTC).
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