Generating two different uniformly distributed points on a sphere using one uniform distribution: Icosahedron V=12.
This applet is used to study the uniformly distribution of geometric medians on a sphere, „induces“ by the discrete sample of uniformly distribution points in the 3-D space. Description is in https://www.geogebra.org/m/y8dnkeuu. Here, the 12 vertices of the Icosahedron "induce" the vertices of the other two polyhedra:
20 ●Dodecahedron← 12 ●Icosahedron →30 ●Icosidodecahedron.
Images and explanations are in https://www.geogebra.org/m/rkpxwceh.