Cayley-Graph\;: \;\fgcolor{ff0000}{a^5=1} \;and \;\fgcolor{0000ff}{b^3=1}

\copyright\;Roman\; Chijner,\; Heidelberg\;2012

f02 = 0.734 (slider from 0 to 1, step 0.001)
f01 = 0.346 (slider from 0 to 1, step 0.001)
α = 1.5707963267948966 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Zoom = 2.8 (slider from 0 to 5, step 0.1)
O1 = (-0.1201286698244473, 0.6236500278873415)
l01 = Sequence(Rotate[O1 + (Zoom; α), 2 * π / 5 * i, O1], i, 0, 5)
O2: Element[l01, 1] + (Element[l01, 1] - O1) * f01
l02 = Sequence(Rotate[Element[l01, 1], 2 * π / 3 * i, O2], i, 0, 2)
an: 2 * Zoom * sin(36°)
gz1 = 0.6180339887498949
gz2: 1 / gz1
an1: an * gz2
V01 = Polygon(l01)
V02 = Polygon(l02)
r02: Zoom * f01
O3: Element[l02, 3] + (Element[l02, 3] - O2) * f02
l03 = Sequence(Rotate[Element[l02, 3], 2 * π / 5 * i, O3], i, 0, 5)
V03 = Polygon(l03)
f03 = 0.3 (slider from 0 to 1, step 0.001)
f04 = 0.867 (slider from 0 to 1, step 0.001)
r03: Zoom * f01 * f02
O4: Element[l03, 2] + (Element[l03, 2] - O3) * f03
r04: Zoom * f01 * f02 * f03
l04 = Sequence(Rotate[Element[l03, 2], 2 * π / 3 * i, O4], i, 0, 2)
V04 = Polygon(l04)
r05: Zoom * f01 * f02 * f03 * f04
f05 = 0.57 (slider from 0 to 1, step 0.001)
O5: Element[l04, 2] + (Element[l04, 2] - O4) * f04
l05 = Sequence(Rotate[Element[l04, 2], 2 * π / 5 * i, O5], i, 0, 5)
V05 = Polygon(l05)
r06: Zoom * f01 * f02 * f03 * f04 * f05
O6: Element[l05, 2] + (Element[l05, 2] - O5) * f05
l06 = Sequence(Rotate[Element[l05, 2], 2 * π / 3 * i, O6], i, 0, 2)
V06 = Polygon(l06)
V16 = Sequence(Rotate[V06, 2 * π / 5 * i, O5], i, 0, 3)
V16' = Mirror(V16, Line[O3, O4])
V05' = Mirror(V05, Line[O3, O4])
V16'' = Sequence(Rotate[{V16, V16'}, 2 * π / 5 * i, O3], i, 0, 3)
V15'' = Sequence(Rotate[{V05, V05'}, 2 * π / 5 * i, O3], i, 0, 3)
V14'' = Sequence(Rotate[V04, 2 * π / 5 * i, O3], i, 0, 3)
V14 = 0
V14''' = Mirror(V14'', Line[O1, O2])
V160 = Sequence(Rotate[{V16'', Mirror[V16'', Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4)
V150 = Sequence(Rotate[{V15'', Mirror[V15'', Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4)
V140 = Sequence(Rotate[{V14'', Mirror[V14'', Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4)
V130 = Sequence(Rotate[{V03, Mirror[V03, Line[O1, O2]]}, 2 * π / 5 * i, O1], i, 0, 4)
V120 = Sequence(Rotate[V02, 2 * π / 5 * i, O1], i, 0, 4)