[size=85] Three parameters are used to transform Platonic Solids faces:[br] t - for truncating, [br] q-similarity transformations,[br] α-angle rotation of faces.[br]With these parameters, using the well-known Expansion and Snub operations applied to a polyhedron, you can explore various polyhedra and get a number of Archimedean Solids.[br] Table of the Archimedean Solids obtained in three-parameter models of transformations of the Platonic Solids faces:[br] [color=#ff0000]Platonic Solids[/color] [color=#ff0000]models[/color] [color=#ff0000]→[/color] [color=#ff0000][url=https://www.geogebra.org/m/t254s6he#material/sqgjd3zn]Tetrahedron[/url][/color] [color=#ff0000] [url=https://www.geogebra.org/m/t254s6he#material/fzxyzfrk]Octahedron[/url][/color] [color=#ff0000][url=https://www.geogebra.org/m/t254s6he#material/esuepvjk]Cube[/url][/color] [color=#ff0000] [url=https://www.geogebra.org/m/t254s6he#material/eqtg5vmx]Icosahedron[/url][/color] [color=#ff0000] [url=https://www.geogebra.org/m/t254s6he#material/tqafjerp]Dodecahedron[/url][/color][br][u]Archimedean Solids[/u] [br]1: Truncated Tetrahedron +[br]2: Cuboctahedron + + +[br]3: Truncated Octahedron + + +[br]4: Truncated Cube + +[br]5: Rhombicuboctahedron + + [br]6: Snub Cube + +[br]7: Icosidodecahedron + +[br]8: Truncated Cuboctahedron + +[br]9: Truncated Icosahedron + +[br]10: Truncated Dodecahedron + +[br]11: Rhombicosidodecahedron + +[br]12: Snub Dodecahedron + +[br]13: Truncated Icosidodecahedron + +[/size]