\copyright\; Roman\; Chijner\;,\;Heidelberg\;2013

Parkettierung mit Davidstern / Tiling with the Star of David

Inspirationsquelle war das Muster aus einem Applet von Noel Lambert/
A source of inspiration was the pattern in an applet by Noel Lambert
http://www.geogebratube.org/material/show/id/32105-Noel Lambert

Zoom = 2.5 (slider from 0 to 15, step 0.5)
E = Point(Circle[(0, 0), Zoom])
l00 = Sequence(Rotate[E, π / 3 * i], i, 0, 6)
V001 = Polygon(l00)
O = (0, 0)
ii = 2 (slider from 1 to 6, step 1)
PP = Element(l00, ii)
V002 = Polygon({Element[l00, 6], Element[l00, 5], O})
V002' = Mirror(V002, O)
n = 4 (slider from 1 to 5, step 1)
V02_1 = Translate({V002, V002'}, Vector[E, O])
V11 = Translate(V02_1, Vector[O, 2 * Element[l00, 2]])
V001' = Translate(V001, Vector[O, 2 * Element[l00, 2]])
V01: {V001, V001'}
E' = Rotate(E, 90*°)
hn: Zoom * cos(30°)
V2: {Translate[V02_1, Vector[O, 2 * Element[l00, 2]]], V02_1}
V401, o, a, b, c, o_1 = Polygon(O, Element[l00, 3], Element[l00, 4], Element[l00, 5], O)
E'' = Translate(O, Vector[O, E'] / Zoom * 2 * hn)
V4010: {V401, Mirror[V401, O]}
V4020: {Translate[V401, Vector[O, Element[l00, 2]]], Translate[V401, Vector[O, Element[l00, 6]]]}
V20 = 0
d = true
lll2 = Sequence(Sequence[Translate[V4020, Vector[E, O] * i + 2 * Vector[O, E'] / Zoom * hn * j], i, -2 * n - 2, 2 * n + 2], j, -n - 1, n + 1)
lll1 = Sequence(Sequence[Translate[V4010, Vector[2 * (Vector[E, O] * i + Vector[O, E'] / Zoom * hn * j)]], i, -n - 1, n + 1], j, -n - 1, n + 1)
llll1 = Sequence(Rotate[V001', π / 3 * i], i, 0, 5)
V02 = Mirror(V002', Line[Element[l00, 2], Element[l00, 3]])
lV02 = Sequence(Rotate[V02, π / 3 * i], i, 0, 5)
lV021 = Sequence(Rotate[Mirror[V02, E''], π / 3 * i], i, 0, 5)
lV023 = Sequence(Rotate[Mirror[V001, E''], π / 3 * i], i, 0, 5)
E''': 2 * E''
lV022 = Sequence(Rotate[Mirror[Element[lV021, 1], E'''], π / 3 * i], i, 0, 5)
ll1 = Sequence(Sequence[Translate[V01, Vector[2 * (Vector[E, O] * i + 2 * Vector[O, E'] / Zoom * hn * j)]], i, -2 * n + 2, 2 * n - 2], j, -n + 1, n - 1)
ll2 = Sequence(Sequence[Translate[V2, Vector[2 * (Vector[E, O] * i + 2 * Vector[O, E'] / Zoom * hn * j)]], i, -2 * n + 1, 2 * n - 2], j, -n + 1, n - 1)
V03 = Mirror(V002, Line[Element[l00, 2], Element[l00, 3]])
ll2d = Sequence(Translate[V03, Vector[2 * (Vector[E, O] * i + Vector[O, E'] / Zoom * hn * (-2 * n))]], i, -2 * n + 2, 2 * n - 2)
ll2c = Sequence(Translate[Translate[V02, Vector[O, 2 * Element[l00, 2]]], Vector[2 * (Vector[E, O] * i + 2 * Vector[O, E'] / Zoom * hn * (n - 1))]], i, -2 * n + 2, 2 * n - 2)