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قائمة الأشكال (رياضيات)

☰ جدول المحتويات

هذه قائمة لبعض  الأشكال   رياضيات .

منحنيات جبرية

منحنيات عقلانية 

درجة 2

درجة 3

درجة 4

درجة 5

  • Quintic of l'Hospital

درجة 6

أسر درجة المتغير 

منحنيات واحدة الجنس

منحنيات مع جنس كبير  من  واحدة

أسر منحنيات مع جنس متغير

منحنيات متعالية

تراكيب دالة متعددة التعريف

منحنيات متولدة بمنحنيات أخرى

منحنيات مكان

Surfaces in 3-space

Minimal surfaces

سطوح لا-أطراف 

سطح درجة ثانية

Pseudospherical surfaces

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

Tessellations

Euclidean tilings
Hyperbolic tilings
Hyperbolic star-tilings

Four-dimensional regular polytopes

Degenerate (spherical)

Non-convex

Tessellations of Euclidean 3-space

Degenerate tessellations of Euclidean 3-space

Tessellations of hyperbolic 3-space

Five-dimensional regular polytopes and higher

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

Tessellations of Euclidean 5-space and higher

Tessellations of hyperbolic 4-space

Tessellations of hyperbolic 5-space

Apeirotopes

Abstract polytopes

Non-regular polytopes

2D with 1D surface

Polygons named for their number of sides

Tilings

Uniform polyhedra

Duals of uniform polyhedra

Johnson solids

Other nonuniform polyhedra

Spherical polyhedra

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

Other

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

Honeycombs

5D with 4D surfaces

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

  • 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

Geometry

Glyphs and symbols

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