Demonstration that all Quadrilaterals Tessellate the Plane

Drag the blue points to your required position

Press play/pause
button below

angle = 106 (slider from 100 to 180, step 3)
F = (9, 2)
G = (19.318164613362285, 6.169327708059075)
I = Midpoint(F, G)
G' = Rotate(G, angle°, I)
f = Ray(I, G')
H = (12.476231782489206, 6.977919769889524)
e = Ellipse(F, G, H)
A = (4.36250756816377, -0.40769210439514464)
B = (13.782418959292249, -0.23720939721293652)
D = (8.806467809566374, 6.355925876173794)
C = Intersect(e, f, 1)
poly1, a, b, c, d = Polygon(A, B, C, D)
M: {{0, -1}, {1, 0}}
matrix1: (M * poly1)
E = Centroid(poly1)
A' = Rotate(A, 3.141592653589793, E)
B' = Rotate(B, 3.141592653589793, E)
C' = Rotate(C, 3.141592653589793, E)
D' = Rotate(D, 3.141592653589793, E)
poly1', a', b', c', d' = Polygon(A', B', C', D')
u = Vector(D', C)
A'' = Translate(A', u)
B'' = Translate(B', u)
C'' = Translate(C', u)
D'' = Translate(D', u)
poly1'', a'', b'', c'', d'' = Polygon(A'', B'', C'', D'')
v = Vector(A, C)
w = Vector(B, D)
list1 = Sequence(Sequence[Polygon[Translate[A, Vector[(i * v) + (j * w)]], Translate[B, Vector[(i * v) + (j * w)]], Translate[C, Vector[(i * v) + (j * w)]], Translate[D, Vector[(i * v) + (j * w)]]], i, -7, 7, 1], j, -7, 7, 1)
list2 = Sequence(Sequence[Polygon[Translate[A'', Vector[(i * v) + (j * w)]], Translate[B'', Vector[(i * v) + (j * w)]], Translate[C'', Vector[(i * v) + (j * w)]], Translate[D'', Vector[(i * v) + (j * w)]]], i, -7, 7, 1], j, -7, 7, 1)
α = Angle(G, I, G')
J = Intersect(e, f, 1)