List of mathematical shapes

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

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, "A"^"n", "A"^{"n" − 1}"B", ..., "B"^"n" are vectors
*circle: x² + y² = "r"²
*ellipse
*parabola
*hyperbola
*plane
*polygon
**chiliagon
**decagon
**enneagon
**googolgon
**hectagon
**heptagon
**hendecagon
**hexagon
**myriagon
**octagon
**pentagon
**quadrilateral
**triangle
*y=f(x): "y" = "f"("x")

3D with 1D surface

*helix: "x" = sin("z") ∧ "y" = cos("z")
*lorenz 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"^"p""B"^"q""C"^"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 (doughnut)
*quadric
**cone
**cylinder
**ellipsoid
***spheroid
****sphere
**hyperboloid
**paraboloid
**sphere

4D with 2D surface

*Klein bottle
*Real projective plane

4D with 3D surface

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

5D with 4D surfaces

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

Fractals

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

Esoteric spaces

*$int\_\{-infin\}^\{infin\}f^\{2\}(x),dx=r^2$
*Wormhole -----------

ee also

*List of mathematical topics