List of mathematical shapes
From Wikipedia, the free encyclopedia
Following is a list of shapes studied in mathematics.
Algebraic curves
Rational curves
Degree 2
Degree 3
Degree 4
Degree 5
- Quintic of l'Hospital[1]
Degree 6
- Astroid
- Atriphtaloid
- Nephroid
- Quadrifolium
Families of variable degree
Curves of genus one
Curves with genus greater than one
Curve families with variable genus
Transcendental curves
- Bowditch curve
- Brachistochrone
- Butterfly curve
- Catenary
- Clélies
- Cochleoid
- Cycloid
- Horopter
- Isochrone
- Isochrone of Huygens (Tautochrone)
- Isochrone of Leibniz[2]
- Isochrone of Varignon[3]
- Lamé curve
- Pursuit curve
- Rhumb line
- Spirals
- Syntractrix
- Tractrix
- Trochoid
Piecewise constructions
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[5]
- Slinky spiral[6]
- Twisted cubic
- Viviani's curve
Surfaces in 3-space
Minimal surfaces
Non-orientable surfaces
Quadrics
Pseudospherical surfaces
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
Fractals
- 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[7]
- 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
 | This section needs additional citations for verification. (April 2018) |
- von Koch curve with random interval
- von Koch curve with random orientation
- polymer shapes
- diffusion-limited aggregation
- Self-avoiding random walk[8]
- Brownian motion
- Lichtenberg figure
- Percolation theory
- Multiplicative cascade
Regular polytopes
Summarize
Perspective
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
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
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)
Non-convex
Tessellation
Three-dimensional regular polytopes
Convex
- Platonic solid
- Tetrahedron, the 3-space Simplex
- Cube, the 3-space hypercube
- Octahedron, the 3-space Cross-polytope
- Dodecahedron
- Icosahedron
Degenerate (spherical)
Non-convex
Tessellations
Euclidean tilings
Hyperbolic tilings
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
Degenerate (spherical)
Non-convex
Tessellations of Euclidean 3-space
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
Tessellations of Euclidean 4-space
Tessellations of Euclidean 5-space and higher
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
Apeirotopes
Abstract polytopes
2D with 1D surface
Summarize
Perspective
- 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
Polygons named for their number of sides
- Monogon — 1 sided
- Digon — 2 sided
- Triangle
- Quadrilateral
- Pentagon
- Hexagon
- Heptagon
- Octagon
- Nonagon
- 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
Uniform polyhedra
- Regular polyhedron
- Platonic solid
- Kepler–Poinsot polyhedron (regular star polyhedra)
- Abstract regular polyhedra (Projective polyhedron)
- Archimedean solid
- Prismatic uniform 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
- 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
Spherical polyhedra
Honeycombs
- 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
- Others
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
- 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
- Convex regular 4-polytope
- 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
- 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
- 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
5D with 4D surfaces
- regular 5-polytope
- 5-dimensional cross-polytope
- 5-dimensional hypercube
- 5-dimensional simplex
- 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
Six dimensions
- 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
Seven dimensions
- 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
Eight dimension
- 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
Nine dimensions
Hyperbolic honeycombs
Ten dimensions
Dimensional families
- Honeycombs
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
- Annulus
- Apollonian circles
- Apollonian gasket
- Arbelos
- Borromean rings
- Circle
- Circular sector
- Circular segment
- Cyclic quadrilateral
- Cycloid
- Epitrochoid
- Ex-tangential quadrilateral
- Horocycle
- Hypotrochoid
- Lune
- Pappus chain
- Peaucellier–Lipkin linkage
- Robbins pentagon
- Salinon
- Semicircle
- Squircle
- Steiner chain
- Tangential quadrilateral
Glyphs and symbols
- Borromean rings
- Crescent
- Vesica piscis
- Arc
- Caustic
- Cissoid
- Conchoid
- Cubic Hermite curve
- Curve of constant width
- hedgehog[9]
- Parametric curve
- Bézier curve
- Spline
- Hermite spline
- Beta spline[citation needed]
- Higher-order spline[citation needed]
- NURBS
- Hermite spline
- Ray
- Reuleaux triangle
- Ribaucour curve[10]
Table of all the Shapes
This is a table of all the shapes above.
| Section | Sub-Section | Sup-Section | Name |
|---|---|---|---|
| Algebraic Curves | ¿ Curves | ¿ Curves | Cubic Plane Curve |
| Quartic Plane Curve | |||
| Rational Curves | Degree 2 | Conic Section(s) | |
| 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 | |||
References
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