[size=85] The coordinates of the polyhedron are taken from the [url=https://www.geogebra.org/m/nygpp5cj]applet[/url]: [i]Polyhedra whose vertices are equivalent and have an extreme distribution on the same sphere. [/i][br] The first applet sorts and finds the vertices, surface segments, faces, and volume of the polyhedron and its dual image.[br] The second applet colors the edges and faces of the polyhedron and its dual image.[br] All applets are in the [url=https://www.geogebra.org/m/zyexvyzt]Book[/url]: [i]Polyhedra with extreme distribution of equivalent vertices :[br] [i][url=https://www.geogebra.org/m/nygpp5cj]Polyhedra whose vertices are equivalent and have an extreme distribution on the same sphere. [/url][/i][br][br][i][i][i][i][i][i][i][i][i][size=85]* n=4: [url=https://www.geogebra.org/m/bhjrekg5]Tetrahedron[/url]; n=6: [url=https://www.geogebra.org/m/bnymhqwa]Octahedron[/url]; n=8: [url=https://www.geogebra.org/m/vwx4ubyg]Cube[/url], [url=https://www.geogebra.org/m/kwyq48gc]Square Antiprism[/url]; n=12: [url=https://www.geogebra.org/m/nzz9tsgn]Icosahedron[/url], [url=https://www.geogebra.org/m/cpam8yvx]Cuboctahedron[/url],T[url=https://www.geogebra.org/m/rhhxz9v9]runcated Tetrahedron[/url]; n=20: [url=https://www.geogebra.org/m/upsdws6c]Dodecahedron[/url]; n=24: [url=https://www.geogebra.org/m/mwzudusy]Biscribed Snub Cube[/url], [url=https://www.geogebra.org/m/mfjzdguf]Truncated Cube[/url], [url=https://www.geogebra.org/m/ysudgda3]Biscribed Truncated Octahedron[/url]; n=30: [url=https://www.geogebra.org/m/f5z2c5x4]Icosidodecahedron[/url]; n=48: [url=https://www.geogebra.org/m/hbfeezeb]Biscribed Truncated Cuboctahedron[/url]; n=60: [url=https://www.geogebra.org/m/uekbrkq3]Biscribed Snub Dodecahedron[/url], [url=https://www.geogebra.org/m/ufxkrwur]Rhombicosidodecahedron[/url], [url=https://www.geogebra.org/m/ga6mbuvh]Biscribed Truncated Icosahedron[/url], [url=https://www.geogebra.org/m/ezz6nedt]Truncated Dodecahedron[/url]; n=120: [url=https://www.geogebra.org/m/rzqaujc4]Biscribed Truncated Icosidodecahedron[/url].[/size][/i][/i][/i][/i][/i][/i][/i][/i][/i][/i][/size]

[size=85] This is a well-known [url=http://dmccooey.com/polyhedra/Icosidodecahedron.html]polyhedron[/url]- [b]Icosidodecahedron[/b][table][tr][td]Vertices:  [/td][td]30  (30[4])[/td][/tr][tr][td]Faces:[/td][td]32  (20 equilateral triangles + 12 regular pentagons)[/td][/tr][tr][td]Edges:[/td][td]60[/td][/tr][/table][/size][size=85] This extreme distribution is obtained by me in the [url=https://www.geogebra.org/m/e7v6eps2]applet[/url]- "Three-parameter model transformations of the Icosahedron. Extreme distributions." -Special Case 5). t=0.5, q=1 and α=0. [/size]