A = (-0.6858116049772164, 5.782011615695129)
B = (-3.375039738686259, 1.3208114558987334)
C = (3.6711549062258064, 0.3410151591210201)
polígono1, c, a, b = Polygon(A, B, C)
D = Point(c)
E = Point(c)
F = Point(a)
G = Point(a)
H = Point(b)
I = Point(b)
d = Line(D, E)
e = Line(F, G)
f = Line(I, H)
A' = Intersect(f, d)
B' = Intersect(e, d)
C' = Intersect(f, e)
α = Angle(C', A', B')
β = Angle(A', B', C')
γ = Angle(B', C', A')
C'' = Rotate(C', α / 3.0, A')
g = Ray(A', C'')
J = Intersect(a, g)
C''' = Mirror(C'', b)
h = Ray(A', C''')
J' = Intersect(a, h)
JJ = If(Defined[J], J, J')
i = Segment(A', JJ)
A'' = Rotate(A', β / 3.0, B')
j = Ray(B, A'')
K = Intersect(b, j)
A''' = Mirror(A'', c)
k = Ray(B, A''')
K' = Intersect(b, k)
KK = If(Defined[K], K, K')
l = Segment(B', KK)
m = AngularBisector(JJ, A', B')
L = Intersect(m, l)
M = Intersect(i, l)
B'' = Rotate(B', γ / 3.0, C')
p = Ray(C, B'')
N = Intersect(c, p)
B''' = Mirror(B'', a)
q = Ray(C, B''')
N' = Intersect(c, q)
NN = If(Defined[N], N, N')
r = Segment(C', NN)
n = AngularBisector(KK, B', C')
O = Intersect(n, r)
t = AngularBisector(NN, C', A')
P = Intersect(t, i)
polígono2, p_1, l_1, o = Polygon(L, O, P)
Q = Intersect(m, a)
R = Intersect(t, c)
S = Intersect(n, b)
s = Segment(A, Q)
a_1 = Segment(C, R)
b_1 = Segment(B, S)

Tool: Morley (triángulo) (command Morley)
Triángulo
Input: polígono1
Output: polígono2

A = (-2.24, 0.02)
B = (1.3, 4.48)
C = (3.62, 0.48)
polígono1, c, a, b = Polygon(A, B, C)
D = Point(c)
E = Point(c)
F = Point(a)
G = Point(a)
H = Point(b)
I = Point(b)
d = Line(D, E)
e = Line(F, G)
f = Line(I, H)
A' = Intersect(f, d)
B' = Intersect(e, d)
C' = Intersect(f, e)
α = Angle(C', A', B')
β = Angle(A', B', C')
γ = Angle(B', C', A')
C''_1 = Rotate(C', α / 3.0, A')
C'' = Rotate(C', 2.0 * α / 3.0, A')
A''_1 = Rotate(A', β / 3.0, B')
A'' = Rotate(A', 2.0 * β / 3.0, B')
B''_1 = Rotate(B', γ / 3.0, C')
B'' = Rotate(B', 2.0 * γ / 3.0, C')
g = Line(A', C'')
h = Line(A', C''_1)
i = Line(B', A''_1)
j = Line(B', A'')
k = Line(C', B'')
l = Line(C', B''_1)
P = Intersect(g, i)
Q = Intersect(j, l)
R = Intersect(h, k)
polígono2, r, p, q = Polygon(P, Q, R)