Vertices 60. Biscribed Truncated Icosahedron(extreme distribution). Images: A critical points scheme for Generating uniformly distributed points on a sphere.
[size=85]The applet illustrates the case where 60 vertices of a Biscribed Truncated Icosahedron -extreme distribution "induce" the vertices of two other polyhedra:[br][b][color=#ff0000]32 ●[url=https://www.geogebra.org/m/g7qhqgva]Pentakis Dodecahedron[/url][/color] ←[color=#0000ff]60 ●[/color][url=https://www.geogebra.org/m/eyg2fedd][color=#0000ff]Biscribed Truncated Icosahedron -extreme distribution[/color][/url] →[color=#6aa84f]90 ☐[/color] [color=#6aa84f]as [url=https://www.geogebra.org/m/at2yxep3]Rectified truncated icosahedron[/url].[/color][/b][br] Description are in [url=https://www.geogebra.org/m/y8dnkeuu]https://www.geogebra.org/m/y8dnkeuu[/url] and [url=https://www.geogebra.org/m/rkpxwceh]https://www.geogebra.org/m/rkpxwceh[/url]. [br] Images and explanations of calculating results from [url=https://www.geogebra.org/m/w8jgrjcf]applet[/url]: Generating two different uniformly distributed points on a sphere using one uniform distribution: Biscribed Truncated Icosahedron V=60:[/size]
“Polyhedra” of critical points:[br] [b]32 ●[color=#ff0000]Pentakis Dodecahedron[/color] ←60 ● [color=#0000ff]Biscribed Truncated Icosahedron -extreme distribution[/color] →90 ☐ [color=#38761d]as Rectified truncated icosahedron [/color][/b]
Isolines, f'ₓ=0, f'ᵧ=0 and the critical points of the distance sum function over a rectangular region: - π ≤φ ≤ π; -π/2≤θ≤π/2.
