friezes

move blue dots

Elements de simetria

T = Point(a)
o: x(T)
r, a_1, b_1, c_1, d_1 = Polygon((0, 60), (13 * o, 60), (13 * o, 68), (0, 68))
B = PointIn(r)
B1: (x(B), y(B))
v10 = Vector((0, -10))
B2 = Translate(B1, v10)
B3 = Translate(B2, v10)
B4: 2 * B3 - B2
B5: 2 * B4 - B3
B6: 2 * B5 - B4
B7: 2 * B6 - B5
B7' = Mirror(B7, y = 4)
E = (1.5518399022707086, 61.11669023697658)
E1: (x(E), y(E))
E2 = Translate(E1, v10)
E3 = Translate(E2, v10)
E4: 2 * E3 - E2
E5: 2 * E4 - E3
E6: 2 * E5 - E4
E7: 2 * E6 - E5
E7' = Mirror(E7, y = 4)
D = (10.94289795368862, 64.37225702813481)
D1: (x(D), y(D))
D2 = Translate(D1, v10)
D3 = Translate(D2, v10)
D4: 2 * D3 - D2
D5: 2 * D4 - D3
D6: 2 * D5 - D4
D7: 2 * D6 - D5
D7' = Mirror(D7, y = 4)
C = (6.184761874303546, 64.99832756489599)
C1: (x(C), y(C))
C2 = Translate(C1, v10)
C3 = Translate(C2, v10)
C4 = Translate(C3, v10)
C5 = Translate(C4, v10)
C6 = Translate(C5, v10)
C7 = Translate(C6, v10)
C7' = Mirror(C7, y = 4)
rv = Line(T, T + v10)
A = PointIn(r)
A1: (x(A), y(A))
A2 = Translate(A1, v10)
A3 = Translate(A2, v10)
A4: 2 * A3 - A2
A5: 2 * A4 - A3
A6: 2 * A5 - A4
A7: 2 * A6 - A5
A7' = Mirror(A7, y = 4)
A_1 = Point(a)
u = Vector(A_1, T)
D' = Translate(D, u)
v = (0.12830339100965915, -0.38491017302897035)
D'' = Translate(D', v)
C'_1 = Translate(C, v10)
D'_1 = Translate(D, v10)
E'_1 = Translate(E, v10)
A' = Translate(A, v10)
B' = Translate(B, v10)
pen1, c'_1, d'_1, e'_1, a', b' = Polygon(C'_1, D'_1, E'_1, A', B')
pen2, a3, b3, c3, d3, e3 = Polygon(A3, B3, C3, D3, E3)
pen3, a4, b4, c4, d4, e4 = Polygon(A4, B4, C4, D4, E4)
pen4, a5, b5, c5, d5, e5 = Polygon(A5, B5, C5, D5, E5)
pen64, k, l, c_2, d_2, e_2 = Polygon(Mirror[A7', rv], Mirror[B7', rv], Mirror[C7', rv], Mirror[D7', rv], Mirror[E7', rv])
pen5, a6, b6, c6, d6, e6 = Polygon(A6, B6, C6, D6, E6)
F = Mirror(C'_1, rv)
G = Mirror(D'_1, rv)
H = Mirror(E'_1, rv)
A'' = Mirror(A', rv)
B'' = Mirror(B', rv)
pen1m, f_2, g_2, h, a'', b'' = Polygon(F, G, H, A'', B'')
SC: (x(T), 44)
A3' = Mirror(A3, SC)
B3' = Mirror(B3, SC)
C3' = Mirror(C3, SC)
D3' = Mirror(D3, SC)
E3' = Mirror(E3, SC)
pen2sc, a3', b3', c3', d3', e3' = Polygon(A3', B3', C3', D3', E3')
A4' = Mirror(A4, j)
B4' = Mirror(B4, j)
C4' = Mirror(C4, j)
D4' = Mirror(D4, j)
E4' = Mirror(E4, j)
pen3mh, a4', b4', c4', d4', e4' = Polygon(A4', B4', C4', D4', E4')
A4'' = Translate(A4', u)
B4'' = Translate(B4', u)
C4'' = Translate(C4', u)
D4'' = Translate(D4', u)
E4'' = Translate(E4', u)
pen3g, a4'', b4'', c4'', d4'', e4'' = Polygon(A4'', B4'', C4'', D4'', E4'')
A5' = Mirror(A5, rv)
B5' = Mirror(B5, rv)
C5' = Mirror(C5, rv)
D5' = Mirror(D5, rv)
E5' = Mirror(E5, rv)
pen4mv, a5', b5', c5', d5', e5' = Polygon(A5', B5', C5', D5', E5')
A5'' = Mirror(A5', i)
B5'' = Mirror(B5', i)
C5'' = Mirror(C5', i)
D5'' = Mirror(D5', i)
E5'' = Mirror(E5', i)
pen4mvh, a5'', b5'', c5'', d5'', e5'' = Polygon(A5'', B5'', C5'', D5'', E5'')
A5'_1 = Mirror(A5, i)
B5'_1 = Mirror(B5, i)
C5'_1 = Mirror(C5, i)
D5'_1 = Mirror(D5, i)
E5'_1 = Mirror(E5, i)
pen4mh, a5'_1, b5'_1, c5'_1, d5'_1, e5'_1 = Polygon(A5'_1, B5'_1, C5'_1, D5'_1, E5'_1)
A5'_2 = Translate(A5, Vector[2 * u])
B5'_2 = Translate(B5, Vector[2 * u])
C5'_2 = Translate(C5, Vector[2 * u])
D5'_2 = Translate(D5, Vector[2 * u])
E5'_2 = Translate(E5, Vector[2 * u])
pen4g1 = Mirror(Polygon[Translate[A5, Vector[2 * u]], Translate[B5, Vector[2 * u]], Translate[C5, Vector[2 * u]], Translate[D5, Vector[2 * u]], Translate[E5, Vector[2 * u]]], y = 24)
pen4g2 = Mirror(Polygon[Translate[A5', Vector[2 * u]], Translate[B5', Vector[2 * u]], Translate[C5', Vector[2 * u]], Translate[D5', Vector[2 * u]], Translate[E5', Vector[2 * u]]], y = 24)
A6' = Mirror(A6, y = 14)
B6' = Mirror(B6, y = 14)
C6' = Mirror(C6, y = 14)
D6' = Mirror(D6, y = 14)
E6' = Mirror(E6, y = 14)
pen5mh, a6', b6', c6', d6', e6' = Polygon(A6', B6', C6', D6', E6')
pen62, a7', b7', c7', d7', e7' = Polygon(A7', B7', C7', D7', E7')
p21 = Sequence(Polygon[Translate[A3, Vector[2 * t * u]], Translate[B3, Vector[2 * t * u]], Translate[C3, Vector[2 * t * u]], Translate[D3, Vector[2 * t * u]], Translate[E3, Vector[2 * t * u]]], t, 1, 5)
p22 = Sequence(Polygon[Translate[A3', Vector[2 * t * u]], Translate[B3', Vector[2 * t * u]], Translate[C3', Vector[2 * t * u]], Translate[D3', Vector[2 * t * u]], Translate[E3', Vector[2 * t * u]]], t, 1, 5)
p11 = Sequence(Polygon[Translate[C'_1, Vector[2 * t * u]], Translate[D'_1, Vector[2 * t * u]], Translate[E'_1, Vector[2 * t * u]], Translate[A', Vector[2 * t * u]], Translate[B', Vector[2 * t * u]]], t, 1, 5)
p12 = Sequence(Polygon[Translate[F, Vector[2 * t * u]], Translate[G, Vector[2 * t * u]], Translate[H, Vector[2 * t * u]], Translate[A'', Vector[2 * t * u]], Translate[B'', Vector[2 * t * u]]], t, 1, 5)
p31 = Sequence(Polygon[Translate[A4, Vector[2 * t * u]], Translate[B4, Vector[2 * t * u]], Translate[C4, Vector[2 * t * u]], Translate[D4, Vector[2 * t * u]], Translate[E4, Vector[2 * t * u]]], t, 1, 5)
p32 = Sequence(Polygon[Translate[A4'', Vector[2 * t * u]], Translate[B4'', Vector[2 * t * u]], Translate[C4'', Vector[2 * t * u]], Translate[D4'', Vector[2 * t * u]], Translate[E4'', Vector[2 * t * u]]], t, 1, 5)
p41 = Sequence(Polygon[Translate[A5, Vector[4 * t * u]], Translate[B5, Vector[4 * t * u]], Translate[C5, Vector[4 * t * u]], Translate[D5, Vector[4 * t * u]], Translate[E5, Vector[4 * t * u]]], t, 1, 2)
p42 = Sequence(Translate[pen4g1, Vector[4 * t * u]], t, 1, 2)
p44 = Sequence(Translate[pen4g2, Vector[4 * t * u]], t, 1, 2)
p43 = Sequence(Polygon[Translate[A5', Vector[4 * t * u]], Translate[B5', Vector[4 * t * u]], Translate[C5', Vector[4 * t * u]], Translate[D5', Vector[4 * t * u]], Translate[E5', Vector[4 * t * u]]], t, 1, 2)
p51 = Sequence(Polygon[Translate[A6, Vector[t * u]], Translate[B6, Vector[t * u]], Translate[C6, Vector[t * u]], Translate[D6, Vector[t * u]], Translate[E6, Vector[t * u]]], t, 1, 11)
p52 = Sequence(Polygon[Translate[A6', Vector[t * u]], Translate[B6', Vector[t * u]], Translate[C6', Vector[t * u]], Translate[D6', Vector[t * u]], Translate[E6', Vector[t * u]]], t, 1, 11)
A6'_1 = Mirror(A6, rv)
B6'_1 = Mirror(B6, rv)
C6'_1 = Mirror(C6, rv)
D6'_1 = Mirror(D6, rv)
E6'_1 = Mirror(E6, rv)
A7'_1 = Mirror(A7, rv)
B7'_1 = Mirror(B7, rv)
C7'_1 = Mirror(C7, rv)
D7'_1 = Mirror(D7, rv)
E7'_1 = Mirror(E7, rv)
pen63, a7'_1, b7'_1, c7'_1, d7'_1, e7'_1 = Polygon(A7'_1, B7'_1, C7'_1, D7'_1, E7'_1)
C' = Translate(C, Vector[6 * v10])
D'_2 = Translate(D, Vector[6 * v10])
E' = Translate(E, Vector[6 * v10])
A'_1 = Translate(A, Vector[6 * v10])
B'_1 = Translate(B, Vector[6 * v10])
pen61, c', d'_2, e', a'_1, b'_1 = Polygon(C', D'_2, E', A'_1, B'_1)
p61 = Sequence(Polygon[Translate[C', Vector[2 * t * u]], Translate[D'_2, Vector[2 * t * u]], Translate[E', Vector[2 * t * u]], Translate[A'_1, Vector[2 * t * u]], Translate[B'_1, Vector[2 * t * u]]], t, 1, 5)
p62 = Sequence(Polygon[Translate[A7', Vector[2 * t * u]], Translate[B7', Vector[2 * t * u]], Translate[C7', Vector[2 * t * u]], Translate[D7', Vector[2 * t * u]], Translate[E7', Vector[2 * t * u]]], t, 1, 5)
p63 = Sequence(Polygon[Translate[A7'_1, Vector[2 * t * u]], Translate[B7'_1, Vector[2 * t * u]], Translate[C7'_1, Vector[2 * t * u]], Translate[D7'_1, Vector[2 * t * u]], Translate[E7'_1, Vector[2 * t * u]]], t, 1, 5)
p64 = Sequence(Translate[pen64, Vector[2 * t * u]], t, 1, 5)
p20 = Sequence(Polygon[Translate[C, Vector[t * u]], Translate[D, Vector[t * u]], Translate[E, Vector[t * u]], Translate[A, Vector[t * u]], Translate[B, Vector[t * u]]], t, 1, 11)
rr = Sequence(Translate[r, Vector[t * v10]], t, 1, 6)
v1 = Vector(A, A + u)
v2 = Vector(A + v10, A + 2 * u + v10)
v3 = Vector(A + 2 * v10, A + 2 * u + 2 * v10)
v4 = Vector(A + 3 * v10, A + 2 * u + 3 * v10)
v5 = Vector(A + 4 * v10, A + 4 * u + 4 * v10)
v6 = Vector(A + 5 * v10, A + u + 5 * v10)
v7 = Vector(A + 6 * v10, A + 2 * u + 6 * v10)
b = Segment((o, 49), (o, 59))
bb = Sequence(Translate[b, Vector[t * u]], t, 1, 11)
sscc = Sequence(Translate[SC, Vector[t * u]], t, 1, 11)
d = Segment((o, 19), (o, 29))
gg = Segment((o, -1), (o, 9))
ddd = Sequence(Translate[d, Vector[t * u]], t, 1, 11)
ggg = Sequence(Translate[gg, Vector[t * u]], t, 1, 11)
v44 = Vector((0, 34), (o, 34))
v55 = Vector((0, 24), (2 * o, 24))
e = false
pen, a_2, b_2, c, d_3, e_1 = Polygon(A, B, C, D, E)