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قائمة الأشكال (رياضيات)

من ويكيبيديا، الموسوعة الحرة
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المحتوى هنا ينقصه الاستشهاد بمصادر. يرجى إيراد مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (مارس 2016)

هذه قائمة لبعض  الأشكال   رياضيات .

محتويات

منحنيات جبرية[عدل]

منحنيات عقلانية [عدل]

درجة 2[عدل]

درجة 3[عدل]

درجة 4[عدل]

درجة 5[عدل]

  • Quintic of l'Hospital

درجة 6[عدل]

أسر درجة المتغير [عدل]

منحنيات واحدة الجنس[عدل]

منحنيات مع جنس كبير  من  واحدة[عدل]

أسر منحنيات مع جنس متغير[عدل]

منحنيات متعالية[عدل]

تراكيب دالة متعددة التعريف[عدل]

منحنيات متولدة بمنحنيات أخرى[عدل]

منحنيات مكان[عدل]

Surfaces in 3-space[عدل]

Minimal surfaces[عدل]

سطوح لا-أطراف [عدل]

سطح درجة ثانية[عدل]

Pseudospherical surfaces[عدل]

سطوح جبرية[عدل]

أنظر  قائمة السطوح الجبرية.

سطوح التأثيرات[عدل]

كسور[عدل]

كسور عشوائية[عدل]

Regular Polytopes[عدل]

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 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 قرص عسل 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[عدل]

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[عدل]

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[عدل]

One-dimensional regular polytope[عدل]

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[عدل]

محدب[عدل]

Degenerate (spherical)[عدل]
  • Henagon
  • Digon

Non-convex[عدل]

فسيفساء [عدل]

Three-dimensional regular polytopes[عدل]

محدب[عدل]

Degenerate (spherical)[عدل]

  • hosohedron
  • dihedron
  • Henagon#In spherical geometry

Non-convex[عدل]

Tessellations[عدل]

Euclidean tilings[عدل]
Hyperbolic tilings[عدل]
Hyperbolic star-tilings[عدل]

Four-dimensional regular polytopes[عدل]

Degenerate (spherical)[عدل]

Non-convex[عدل]

Tessellations of Euclidean 3-space[عدل]

Degenerate tessellations of Euclidean 3-space[عدل]

Tessellations of hyperbolic 3-space[عدل]

Five-dimensional regular polytopes and higher[عدل]

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[عدل]

Tessellations of Euclidean 5-space and higher[عدل]

Tessellations of hyperbolic 4-space[عدل]

Tessellations of hyperbolic 5-space[عدل]

Apeirotopes[عدل]

Abstract polytopes[عدل]

Non-regular polytopes[عدل]

2D with 1D surface[عدل]

Polygons named for their number of sides

Tilings[عدل]

Uniform polyhedra[عدل]

Duals of uniform polyhedra[عدل]

Johnson solids[عدل]

Other nonuniform polyhedra[عدل]

Spherical polyhedra[عدل]

Honeycombs[عدل]

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[عدل]

Regular and uniform compound polyhedra[عدل]

  • 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[عدل]

5D with 4D surfaces[عدل]

Honeycombs[عدل]

Six dimensions[عدل]

  • 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[عدل]

  • 6-cubic honeycomb
  • 6-simplex honeycomb
  • 6-demicubic honeycomb
  • 222 honeycomb

Seven dimensions[عدل]

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[عدل]

  • 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[عدل]

  • 10-cube
  • 10-demicube
  • 10-orthoplex
  • 10-simplex

Dimensional families[عدل]

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

Geometry[عدل]

Glyphs and symbols[عدل]