Goldberg (3,0)
For the GeoGebra worksheet below I used data from this website:
Truncated Pentakis Dodecahedron
Coordinates
22 constants are presented that are easy to reduce up to 7.
(Based on the symmetry of a dodecahedron)
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 )