\Gamma

C_{1} = (-1.9880032204805143, 2.342263023005417)
F' = (2.4467446762791476, 1.5266772029116853)
F = (-2.8035890405742454, 0.5581690415503785)
c = Ellipse(F, F', C_{1})
S_1, S_2, S'_1, S'_2 = Vertex(c)
O = Center(c)
A: S_1 + S'_2 - O
f = Segment(S'_2, S'_1)
g = Segment(S_1, S_2)
B = Mirror(A, S'_2)
C = Mirror(B, S_2)
D = Mirror(C, S'_1)
h = Segment(A, B)
i = Segment(B, C)
j = Segment(C, D)
k = Segment(D, A)
l = Line(A, O)
m = Line(B, D)
P = (-0.41578143128984557, -0.09311741053795666)
n = OrthogonalLine(P, m)
V = Intersect(l, n)
p = OrthogonalLine(P, l)
U = Intersect(m, p)
Ω = Midpoint(V, U)
q = Line(Ω, f)
r = Line(Ω, g)
P' = Mirror(P, Ω)
O' = Mirror(O, Ω)
s = Line(P', O')
E = Intersect(q, s)
G = Intersect(s, r)
H = Midpoint(G, Ω)
t = Line(P', H)
I = Intersect(q, t)
J = Midpoint(I, H)
P'' = Mirror(P', J)
d = Conic(P'', P', O', P, O)
P_4, P_3, P_2, P_1 = Intersect(c, d)
n_1 = OrthogonalLine(P_1, Tangent[P_1, c])
n_2 = OrthogonalLine(P_2, Tangent[P_2, c])
n_3 = OrthogonalLine(P_3, Tangent[P_3, c])
n_4 = OrthogonalLine(P_4, Tangent[P_4, c])
a = Segment(V, U)
K = Point(d)