Truncated Icosahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 3rd-order segments
[size=85]A polyhedron is constructed whose V=60 vertices are the points of the trisection of the segments the same length 3rd-order(g=3) of the [url=https://www.geogebra.org/m/hczvuvhg]Biscribed Pentakis Dodecahedron[/url]. [br] Geometric Constructions are in [url=https://www.geogebra.org/m/p4a5zccm]Applet[/url]: Series of polyhedra obtained by trisection (truncation) different segments of the original polyhedron, and the resulting polyhedra in [url=https://www.geogebra.org/m/uej4qnte]Applet[/url]: Serie of polyhedra obtained by trisection (truncation) segments of the Biscribed Pentakis Dodecahedron.[/size]
1. Generating Elements of mesh modeling the surfaces of convex polyhedron and its dual image
2. Coloring edges and faces of polyhedra
Properties of polyhedra
[size=85]Truncated icosahedron:[br][url=https://en.wikipedia.org/wiki/Truncated_icosahedron]https://en.wikipedia.org/wiki/Truncated_icosahedron[/url][br][url=http://dmccooey.com/polyhedra/TruncatedIcosahedron.html]http://dmccooey.com/polyhedra/TruncatedIcosahedron.html[/url][br]Vertices: 60 (60[3])[br]Faces: 32 (12 regular pentagons + 20 regular hexagons)[br]Edges: 90[br][br]Pentakis dodecahedron:[br][url=https://en.wikipedia.org/wiki/Pentakis_dodecahedron]https://en.wikipedia.org/wiki/Pentakis_dodecahedron[/url][br][url=http://dmccooey.com/polyhedra/PentakisDodecahedron.html]http://dmccooey.com/polyhedra/PentakisDodecahedron.html[/url][br] Vertices: 32 (12[5] + 20[6])[br]Faces: 60 (isosceles triangles)[br]Edges: 90 (60 short + 30 long)[/size]