q1 = Polygon({((-sqrt(2)), 0), (sqrt(2), 0), (sqrt(2), -2), ((-sqrt(2)), -2)})
L_1: {Segment[(((-sqrt(2))) / 2, -1), (sqrt(2) / 2, -1)]}
L_2 = Union(Dilate[L_1, 0.5], Union[Translate[Dilate[L_1, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[L_1, 0.5], (((-sqrt(2))) / 2, -1)]])
L_3 = Union(Dilate[L_2, 0.5], Union[Translate[Dilate[L_2, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[L_2, 0.5], (((-sqrt(2))) / 2, -1)]])
L_4 = Union(Dilate[L_3, 0.5], Union[Translate[Dilate[L_3, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[L_3, 0.5], (((-sqrt(2))) / 2, -1)]])
L_5 = Union(Dilate[L_4, 0.5], Union[Translate[Dilate[L_4, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[L_4, 0.5], (((-sqrt(2))) / 2, -1)]])
M_1: {Segment[(((-sqrt(2))) / 2, -1), (((-sqrt(2))) / 2, -2)], Segment[(sqrt(2) / 2, -1), (sqrt(2) / 2, -2)], Segment[(0, 0), (0, -1)]}
M_2 = Union(Dilate[M_1, 0.5], Union[Translate[Dilate[M_1, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[M_1, 0.5], (((-sqrt(2))) / 2, -1)]])
M_3 = Union(Dilate[M_2, 0.5], Union[Translate[Dilate[M_2, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[M_2, 0.5], (((-sqrt(2))) / 2, -1)]])
M_4 = Union(Dilate[M_3, 0.5], Union[Translate[Dilate[M_3, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[M_3, 0.5], (((-sqrt(2))) / 2, -1)]])
M_5 = Union(Dilate[M_4, 0.5], Union[Translate[Dilate[M_4, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[M_4, 0.5], (((-sqrt(2))) / 2, -1)]])
N_1: {Segment[(0, -1), (0, -2)]}
N_2 = Union(Dilate[N_1, 0.5], Union[Translate[Dilate[N_1, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[N_1, 0.5], (((-sqrt(2))) / 2, -1)]])
N_3 = Union(Dilate[N_2, 0.5], Union[Translate[Dilate[N_2, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[N_2, 0.5], (((-sqrt(2))) / 2, -1)]])
N_4 = Union(Dilate[N_3, 0.5], Union[Translate[Dilate[N_3, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[N_3, 0.5], (((-sqrt(2))) / 2, -1)]])
N_5 = Union(Dilate[N_4, 0.5], Union[Translate[Dilate[N_4, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[N_4, 0.5], (((-sqrt(2))) / 2, -1)]])
M_6 = Union(Dilate[M_5, 0.5], Union[Translate[Dilate[M_5, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[M_5, 0.5], (((-sqrt(2))) / 2, -1)]])
N_6 = Union(Dilate[N_5, 0.5], Union[Translate[Dilate[N_5, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[N_5, 0.5], (((-sqrt(2))) / 2, -1)]])
L_6 = Union(Dilate[L_5, 0.5], Union[Translate[Dilate[L_5, 0.5], (sqrt(2) / 2, -1)], Translate[Dilate[L_5, 0.5], (((-sqrt(2))) / 2, -1)]])