قائمة الأشكال (رياضيات)

هذه قائمة لبعض  الأشكال   رياضيات .

منحنيات جبرية

درجة 2

درجة 5
  • Quintic of l'Hospital

درجة 6
  • منحنى نجمي ‏
  • Atriphtaloid
  • Nephroid
  • Quadrifolium

أسر درجة المتغير 

منحنيات واحدة الجنس

منحنيات مع جنس كبير  من  واحدة
  • Butterfly curve (algebraic)
  • Elkies trinomial curves
  • Hyperelliptic curve
  • Klein quartic
  • Classical modular curve
  • Bolza surface
  • Macbeath surface

أسر منحنيات مع جنس متغير

منحنيات متعالية

تراكيب دالة متعددة التعريف

منحنيات مكان
  • Conchospiral
  • لولب (رياضيات)
    • 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

Minimal surfaces
  • Catalan's minimal surface
  • سطح أصغري
  • Catenoid
  • Enneper surface
  • Gyroid
  • سطح حلزوني
  • Lidinoid
  • Riemann's minimal surface
  • Saddle tower
  • Scherk surface
  • Schwarz minimal surface
  • Triply periodic minimal surface

سطوح لا-أطراف 

سطح درجة ثانية

Pseudospherical surfaces
  • Dini's surface
  • Pseudosphere

سطوح جبرية

أنظر  قائمة السطوح الجبرية.

سطوح التأثيرات

كسور

كسور عشوائية

Regular Polytopes

This table shows a summary of regular polytope counts by dimension.

بعد محدب 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 ∞ مضلع ∞ قائمة الأشكال 1 1 0 0 ∞
3 5 قائمة الأشكال 4 قائمة الأشكال 3 قائمة الأشكال ∞ ∞ ∞ ∞
4 6 قائمة الأشكال 10 قائمة الأشكال 1 قرص عسل 4 0 11 ∞
5 3 قائمة الأشكال 0 3 قائمة الأشكال 5 4 2 ∞
6 3 قائمة الأشكال 0 1 قائمة الأشكال 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

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

محدب
Degenerate (spherical)
  • Henagon
  • Digon

Non-convex

فسيفساء 

Three-dimensional regular polytopes

محدب

Degenerate (spherical)
  • hosohedron
  • dihedron
  • Henagon#In spherical geometry

Non-convex
  • Kepler–Poinsot polyhedra
    • Small stellated dodecahedron
    • Great dodecahedron
    • Great stellated dodecahedron
    • Great icosahedron
Euclidean tilings
Hyperbolic tilings
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 مهيكل ‏
    • تسراكت, the 4-space مكعب زائدي ‏
    • 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 (geometry)
  • 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
  • Order-2 triangular tiling
  • Order-2 hexagonal tiling

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
  • خماسي الأبعاد ‏
  • Honeycomb (geometry)
  • tetracomb
مهيكل ‏ مكعب زائدي ‏ 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 المكعب المفرط 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
  • مكعب زائدي ‏
  • 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

Abstract polytopes
  • Abstract polytope
    • 11-cell
    • 57-cell

2D with 1D surface

Polygons named for their number of sides

Tilings
  • List of uniform tilings
  • Uniform tilings in hyperbolic plane
  • Archimedean tiling
    • Square tiling
    • تبليط مثلثي
    • 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

Duals of uniform polyhedra
  • مجسم كاتالان ‏
    • triakis tetrahedron
    • ذو إثنا عشر وجهًا معينيًا ‏
    • Triakis octahedron
    • Tetrakis hexahedron
    • Deltoidal icositetrahedron
    • Disdyakis dodecahedron
    • Pentagonal icositetrahedron
    • Rhombic triacontahedron
    • Triakis icosahedron
    • Pentakis dodecahedron
    • Deltoidal hexecontahedron
    • Disdyakis triacontahedron
    • Pentagonal hexecontahedron
  • non-convex

Other nonuniform polyhedra

Spherical polyhedra
  • Dihedron
  • Hosohedron

Honeycombs
Convex uniform honeycomb
Dual uniform honeycomb
Others
  • Trapezo-rhombic dodecahedral honeycomb
  • Weaire–Phelan structure
  • Order-4 dodecahedral honeycomb
  • Order-5 cubic honeycomb
  • Order-5 dodecahedral honeycomb
  • Icosahedral honeycomb

Regular and uniform compound polyhedra
  • 4-polytope
    • hecatonicosachoron
    • hexacosichoron
    • hexadecachoron
    • icositetrachoron
    • pentachoron
    • tesseract
  • spherical cone
Convex regular 4-polytope
  • 5-cell, Tesseract, 16-cell, 24-cell, 120-cell, 600-cell
Abstract regular polytope
  • 11-cell, 57-cell
  • 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
  • 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

5D with 4D surfaces

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
  • 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
  • 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

Ten dimensions
  • 10-cube
  • 10-demicube
  • 10-orthoplex
  • 10-simplex

Dimensional families
  • Simplex
  • Hypercube
  • Cross-polytope
Uniform polytope
  • Demihypercube
  • Uniform 1k2 polytope
  • Uniform 2k1 polytope
  • Uniform k21 polytope
Honeycombs
  • Hypercubic honeycomb
  • Alternated hypercubic honeycomb

Glyphs and symbols
  • بوابة رياضيات
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