Goldberg (3,0)

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