A spherical kaleidoscope is a Schwarz triangle (p,q,r) with 1/p+1/q+1/r > 1. (2,2,n) is the infinite family; tetra/octa/icosa are the only three exceptions. Schwarz adds fractional angles (5⁄2…) — same mirrors, a triangle that wraps the sphere d>1 times → star tilings. Flip on the pen and draw: each stroke folds into the fundamental domain, so it reflects into every cell at once. Want lobes into space? → build.