Props made to accompany a course in linear analysis. Each of these shapes shows a unit ball in a different Lᵖ norm, stretched in the x axis.

• Ellipsoid: (x/2)² + y² + z² ≤ 1 (the L² norm)
• Cuboid: max(|x/2|,|y|,|z|) ≤ 1 (the L^∞ norm)
• Stretched octahedron: |x/2| + |y| + |z| ≤ 1 (the L¹ norm)
• Squircle-oid: (x/2)⁴ + y⁴ + z⁴ ≤ 1 (the L⁴ norm)

I wrote some Python code in Blender to produce the mesh for the squircle-oid. It samples points along the x interval (-1,1), then finds corresponding y and z values. Finally, it finds the convex hull of all the sampled points.