For the GeoGebra worksheet below I used data from this website:[br][url=http://dmccooey.com/polyhedra/DualGeodesicIcosahedron4.html][b][color=#0000ff]Truncated Pentakis Dodecahedron[br][/color][/b][/url][url=http://dmccooey.com/polyhedra/DualGeodesicIcosahedron4.txt][b][color=#0000ff]Coordinates[/color][/b][/url][br][br]22 constants are presented that are easy to reduce up to 7.[br](Based on the symmetry of a dodecahedron)

[b]Script[br][/b][br]A = ( -21 - 16*sqrt(3) - sqrt(5) + 20*sqrt(15) ) / 218[br]B = ( -48 - 21*sqrt(3) + 60*sqrt(5) - sqrt(15) ) / 218[br]C = ( 63 - 61*sqrt(3) + 3*sqrt(5) + 49*sqrt(15) ) / 654[br]D = ( 240 - 4*sqrt(3) +27*sqrt(5) + 5*sqrt(15) ) / 327[br]E = ( -24 + 30*sqrt(5) ) / 109[br]F = ( 21 + qrt(5) ) / 218[br]G = ( 80 + 9*sqrt(5) ) / 109[br][br]hex = Polygon({ (0,A,1), (B,C,D), (E,F,G), (E,-F,G), (B,-C,D), (0,-A,1) })[br]as = Line( (0,0,0), (1,0,(sqrt(5)+1)/2) )[br]L5 = Sequence( Rotate( hex, k*72°, as ), k,0,4 )[br][br]L5r = Rotate( L5, 180°, zAxis )[br]L25 = Sequence( Rotate( L5r , k*72°, as), k,0,4 )[br]L30 = Join( L5, L25 )[br]L60 = Join( L30, Reflect( L30, (0,0,0) ) )[br][br][br]SetLineThickness( L60, 2 )[br]SetColor( L60, "Orange" )[br]SetFilling( L60, 1 )[br][br]L60'=Dilate( L60, 0.99 )[br]SetColor( L60', "Red" )[br][br]Lobj = { "as", "hex", "L5", "L5r", "L25", "L30" }[br]Execute( Zip( "SetVisibleInView("+obj+", -1, false)", obj,Lobj ) )[br][br]SetActiveView(-1)[br]CenterView( (0,0,0) )[br]SetBackgroundColor( "Black" )[br]SetSpinSpeed( 2 )[br]