Two ways to play with spherical symmetry. A 2D kaleidoscope pen has a
cyclic group Cn; lift it to the sphere and
you get the spherical reflection groups — the (2,2,n) dihedral family,
the three Platonic exceptions, and the star Schwarz triangles. Pick a vibe:
The spherical kaleidoscope. Choose a symmetry group, then draw — every stroke folds into the fundamental cell and reflects into all the others. Calm, flat, beautiful.
Turn symmetry into geometry. Drive a radial height field with weird math — spherical harmonics, gyroid, quasicrystal, fBm noise, superformula — or draw lobes by hand, then export a watertight STL.
(p,q,r) with 1/p+1/q+1/r > 1. Solve that over the
integers and the complete list is one infinite family (2,2,n) plus
exactly three exceptions — tetra (2,3,3), octa (2,3,4), icosa (2,3,5). Both
toys fold the whole sphere into one of those triangles; Sketch paints there,
Build evaluates math there. Either way the result is symmetric for free.