applications.collages.collageAlgebra:
  { 
  
    ntColour = const(.8),
    w = const(tan(22.5)),
    
    f1 = rotate(0),
    f2 = rotate(45),
    f3 = rotate(90),
    f4 = rotate(135),
    f5 = rotate(180),
    f6 = rotate(225),
    f7 = rotate(270),
    f8 = rotate(315),
    F = <f1, f2, f3, f4, f5, f6, f7, f8>,
    
    g1 = scale(.5),
    g2 = scale(.5) . translate(-(sqrt(1/2) - 1/2),.5),
    g3 = scale(.5,-.5) . translate(0,1),
    g4 = scale(.5) . translate(sqrt(1/2) - 1/2,.5),
    G = <g1, g2, g3, g4>,

    p1 = { filledPolygon((-#w / 3,1/3), (#w / 3,1/3), (2/3*#w,2/3), (0,1),
                         (-2/3*#w,2/3)),
           polygon((0,0),(-#w,1),(#w,1))
         },
    
    p2 = { filledPolygon((-#w / 3,1/3), (#w / 3,1/3), (2/3*#w,2/3), (0,1),
                         (-2/3*#w,2/3)),
           polygon((0,0),(-#w,1),(#w,1))
         },
    
    tri1 = { filledPolygon((0,0),(-#w,1),(#w,1))[1,#ntColour,1],
             polygon((0,0),(-#w,1),(#w,1)) },
    tri2 = { filledPolygon((0,0),(-#w,1),(#w,1))[#ntColour,1,1],
             polygon((0,0),(-#w,1),(#w,1)) }
    
  }
