List of mathematical shapes

From Wikipedia, the free encyclopedia

Following is a list of some mathematically well-defined shapes. See also list of polygons, polyhedra and polytopes and list of geometric shapes.

Contents 1 0D with no surface 2 1D with 0D surface 3 2D with 1D surface 4 3D with 1D surface 5 3D with 2D surface 6 4D with 2D surface 7 4D with 3D surface 8 5D with 4D surfaces 9 6D 10 7D 11 8D 12 Fractals 13 Esoteric spaces 14 See also

[edit] 0D with no surface

• point

[edit] 1D with 0D surface

• interval
• line

[edit] 2D with 1D surface

• Bézier curve: (As + Bt)ⁿ | 0 ≤ s ≤ 1 ∧ 0 ≤ t ≤ 1 ∧ s + t = 1, Aⁿ, A^n − 1B, ..., Bⁿ are vectors
• circle: x² + y² = r²
• ellipse
• parabola
• hyperbola
• plane
• polygon
  • chiliagon
  • decagon
  • enneagon
  • googolgon
  • hectagon
  • heptagon
  • hendecagon
  • hexagon
  • myriagon
  • octagon
  • pentagon
  • quadrilateral
  • triangle
• y=f(x): y = f(x)

[edit] 3D with 1D surface

• helix: x = sin(z) ∧ y = cos(z)
• lorenz attractor

[edit] 3D with 2D surface

• Bézier triangle: (As + Bt + Cu)ⁿ | 0 ≤ s ≤ 1 ∧ 0 ≤ t ≤ 1 ∧ 0 ≤ u ≤ 1 ∧ s + t + u = 1, A^pB^qC^r vectors if p + q + r = n and p, q, r are nonnegative integers
• cylinder
• hyperplane
• möbius strip
• platonic solid
  • dodecahedron
  • hexahedron (cube)
  • icosahedron
  • octahedron
  • tetrahedron
• torus
• quadric
  • cone
  • cylinder
  • ellipsoid
    • spheroid
      • sphere
  • hyperboloid
  • paraboloid
  • sphere

[edit] 4D with 2D surface

• Klein bottle
• real projective plane

[edit] 4D with 3D surface

• duocylinder
• hypersphere
• polychoron
  • hecatonicosachoron
  • hexacosichoron
  • hexadecachoron
  • icositetrachoron
  • pentachoron (simplex)
  • tesseract
• spherical cone

[edit] 5D with 4D surfaces

• regular 5-polytopes:
  • 5-dimensional simplex
  • 5-dimensional cross-polytope
  • 5-dimensional measure polytope (5-hypercube)

[edit] 6D

[edit] 7D

[edit] 8D

[edit] Fractals

• Apollonian gasket
• Cantor set
• Dragon curve
• Koch snowflake
• Lévy C curve
• Lyapunov fractal
• Mandelbrot set
• Sierpinski carpet
• Peano curve
• Sierpinski triangle

[edit] Esoteric spaces

• 
• Wormhole

[edit] See also

• List of mathematical topics