List of mathematical shapes

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

Esoteric spaces

• Don't know if this has a name[?]: <math>\int_{-\infin}^{\infin}f^{2}(x)dx=r^2</math>
• wormhole

See also: List of mathematical topics