- Source: List of mathematical shapes
Following is a list of some mathematically well-defined shapes.
Algebraic curves
Cubic plane curve
Quartic plane curve
Fractal
= Rational curves
=Degree 2
Conic sections
Unit circle
Unit hyperbola
Degree 3
Degree 4
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
Golden 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
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
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
= Random fractals
=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.
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
Enneagrammic-order enneagonal tiling
= 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
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
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
= 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
=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
= 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
= Johnson solids
== 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
=Dihedron
Hosohedron
= Honeycombs
=Convex uniform 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
== Regular and uniform compound polyhedra
=Polyhedral compound and Uniform polyhedron compound
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.
= 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
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
8-demicube, Truncated 8-demicube, Cantellated 8-demicube, Runcinated 8-demicube, Stericated 8-demicube, Pentellated 8-demicube, Hexicated 8-demicube
142 polytope, 241 polytope, 421 polytope, Truncated 421 polytope, Truncated 241 polytope, Truncated 142 polytope, Cantellated 421 polytope, Cantellated 241 polytope, Runcinated 421 polytope
= 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
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
Glyphs and symbols
Table of all the Shapes
This is a table of all the shapes above.
References
Kata Kunci Pencarian:
- Sistem saraf
- Andrew Gelman
- Matematika dan arsitektur
- List of mathematical shapes
- Lists of shapes
- List of two-dimensional geometric shapes
- Lists of mathematics topics
- List of mathematical examples
- Mathematical object
- Glossary of mathematical symbols
- Hearing the shape of a drum
- Mathematics
- Mathematical operators and symbols in Unicode
