Generating two different uniformly distributed points on a sphere using one uniform distribution: Icosidodecahedron V=30.
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 30 vertices of the Icosidodecahedron "induce" the vertices of the other two polyhedra:
V=32 ●Pentakis Dodecahedron← V=30 ●Icosidodecahedron →V=60 ☐Rhombicosidodecahedron.
Images and explanations are in https://www.geogebra.org/m/pudk8trx and https://www.geogebra.org/m/rkpxwceh.