[nrzeevuv] Finite shapes

July 21, 2019

Some compact manifolds chosen for elegance and practicality.

2D

  • Equilateral triangle: 1 degree of freedom in shape, namely size

  • Rectangle: 2 degrees of freedom. Rectangles of various aspects ratios are useful practically.

  • Circle (actually disc): 1 degree of freedom

  • Sphere surface: 1 degree of freedom

  • Box surface: 3 degrees of freedom

  • Rectangular tiling (flat torus): 2 degrees of freedom

  • Regular hexagonal tiling: 1 degree of freedom

Others: various special triangles, regular and irregular polygons, ellipse, other tilings, surfaces of regular and irregular polyhedra, ellipsoids, torus in 3 space, hemisphere, cylinder side (truncated so as not to be infinite), cone, two cones joined at bases, sphericon.

3D

We limit to Euclidean space for practicality.

  • Regular tetrahedron

  • Box

  • Sphere (actually ball)

  • Box honeycomb

Others not already listed above: various special tetrahedra, square pyramids, Kelvin cell honeycomb, rhombic dodecahedron honeycomb.

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