List of mathematical shapes

Following is a list of some mathematically well-defined shapes.

Table of contents

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

no D with no surface

• empty set

0D with no surface

• point

1D with 0D surface

• interval
• line

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
  • decagon
  • googolgon
  • heptagon
  • hexagon
  • megagon
  • nonagon
  • octagon
  • pentagon
  • square
  • triangle
  • umdecagon
• y=f(x): y=f(x)

3D with 1D surface

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

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

4D with 2D surface

• klein bottle

4D with 3D surface

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

5D

6D

7D

8+ D

Fractals

• Cantor set
• Dragon curve
• Koch snowflake
• Lyapunov fractal
• Mandelbrot set
• Sierpinski carpet
• Peano curve
• Sierpinski triangle

Esoteric spaces

• Don't know if this has a name:
• wormhole

See also: List of mathematical topics