Pentomino mit einem Symmetriezentrum - Typ 10
Author: Mag. G. Wengler

Dieser Typ ist 1-fach zentrisch. Überlege, wie viele unterschiedliche Positionen es deshalb gibt.

hat 1 Zentrum

drehen

zentrisches Pentomino

A = (-3, 6)
a = 0
b = -1
B: (a + x(A), b + y(A))
c = 1
d = -1
C: (c + x(A), d + y(A))
e = 1
f = -3
D: (e + x(A), f + y(A))
g = 3
h = -3
E: (g + x(A), h + y(A))
i = 3
j = -2
F: (i + x(A), j + y(A))
k = 2
l = -2
G: (k + x(A), l + y(A))
m = 2
n = -1
H: (m + x(A), n + y(A))
o = 2
p = 0
I: (o + x(A), p + y(A))
q = 1
r = 0
J: (q + x(A), r + y(A))
Vieleck1, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1, j_1 = Polygon(A, B, C, D, E, F, G, H, I, J)
t = false
M = (2, 5)
u = 0
v = -1
N: (u + x(M), v + y(M))
w_4 = 1
z = -1
O: (w_4 + x(M), z + y(M))
l_1 = 1
m_1 = -2
P: (l_1 + x(M), m_1 + y(M))
n_1 = 2
o_1 = -2
Q: (n_1 + x(M), o_1 + y(M))
p_1 = 2
q_1 = -3
R: (p_1 + x(M), q_1 + y(M))
r_1 = 3
s_1 = -3
S: (r_1 + x(M), s_1 + y(M))
t_1 = 3
u_1 = -1
T: (t_1 + x(M), u_1 + y(M))
v_1 = 2
w_1 = -1
U: (v_1 + x(M), w_1 + y(M))
z_1 = 2
a_2 = 0
V: (z_1 + x(M), a_2 + y(M))
Vieleck2, m_2, n_2, p_2, q_2, r_2, s_2, t_2, b_5, d_5, e_5 = Polygon(Rotate[A, 270*°, (1.5, 1.5)], Rotate[B, 270*°, (1.5, 1.5)], Rotate[C, 270*°, (1.5, 1.5)], Rotate[D, 270*°, (1.5, 1.5)], Rotate[E, 270*°, (1.5, 1.5)], Rotate[F, 270*°, (1.5, 1.5)], Rotate[G, 270*°, (1.5, 1.5)], Rotate[H, 270*°, (1.5, 1.5)], Rotate[I, 270*°, (1.5, 1.5)], Rotate[J, 270*°, (1.5, 1.5)])
W = (4, 1)
b_2 = 1
c_2 = 0
Z: (b_2 + x(W), c_2 + y(W))
d_2 = 1
e_2 = -2
A_1: (d_2 + x(W), e_2 + y(W))
f_2 = 0
g_2 = -2
B_1: (f_2 + x(W), g_2 + y(W))
h_2 = 0
i_2 = -3
C_1: (h_2 + x(W), i_2 + y(W))
j_2 = -2
k_2 = -3
D_1: (j_2 + x(W), k_2 + y(W))
l_2 = -2
w_2 = -2
E_1: (l_2 + x(W), w_2 + y(W))
z_2 = -1
a_3 = -2
F_1: (z_2 + x(W), a_3 + y(W))
b_3 = -1
c_3 = -1
G_1: (b_3 + x(W), c_3 + y(W))
d_3 = 0
e_3 = -1
H_1: (d_3 + x(W), e_3 + y(W))
Vieleck3, f_3, g_3, h_3, a_4, b_4, c_4, d_4, e_4, f_5, g_5 = Polygon(Rotate[A, 180*°, (1.5, 1.5)], Rotate[B, 180*°, (1.5, 1.5)], Rotate[C, 180*°, (1.5, 1.5)], Rotate[D, 180*°, (1.5, 1.5)], Rotate[E, 180*°, (1.5, 1.5)], Rotate[F, 180*°, (1.5, 1.5)], Rotate[G, 180*°, (1.5, 1.5)], Rotate[H, 180*°, (1.5, 1.5)], Rotate[I, 180*°, (1.5, 1.5)], Rotate[J, 180*°, (1.5, 1.5)])
I_1 = (1, -2)
i_3 = -2
j_3 = 0
J_1: (i_3 + x(I_1), j_3 + y(I_1))
k_3 = -2
l_3 = 1
K_1: (k_3 + x(I_1), l_3 + y(I_1))
m_3 = -3
n_3 = 1
L_1: (m_3 + x(I_1), n_3 + y(I_1))
o_3 = -3
p_3 = 3
M_1: (o_3 + x(I_1), p_3 + y(I_1))
q_3 = -2
r_3 = 3
N_1: (q_3 + x(I_1), r_3 + y(I_1))
s_3 = -2
t_3 = 2
O_1: (s_3 + x(I_1), t_3 + y(I_1))
u_3 = -1
v_3 = 2
P_1: (u_3 + x(I_1), v_3 + y(I_1))
f_4 = -1
g_4 = 1
Q_1: (f_4 + x(I_1), g_4 + y(I_1))
h_4 = 0
i_4 = 1
R_1: (h_4 + x(I_1), i_4 + y(I_1))
Vieleck4, j_4, k_4, l_4, m_4, n_4, p_4, q_4, r_4, h_5, i_5 = Polygon(Rotate[A, 90*°, (1.5, 1.5)], Rotate[B, 90*°, (1.5, 1.5)], Rotate[C, 90*°, (1.5, 1.5)], Rotate[D, 90*°, (1.5, 1.5)], Rotate[E, 90*°, (1.5, 1.5)], Rotate[F, 90*°, (1.5, 1.5)], Rotate[G, 90*°, (1.5, 1.5)], Rotate[H, 90*°, (1.5, 1.5)], Rotate[I, 90*°, (1.5, 1.5)], Rotate[J, 90*°, (1.5, 1.5)])
S_1 = (2, 2)
T_1 = (5, 5)
U_1 = (2, 1)
V_1 = (5, -2)
W_1 = (-2, -2)
Z_1 = (1, 1)
u_4 = false
A_2 = (1.5, 1.5)
c_5 = Circle(A_2, A)
w = 0.7853981633974483 rad (slider from 0 to 6.28318530717959, step 0.017453292519943295)
A' = Rotate(A, w, (1.5, 1.5))
B' = Rotate(B, w, (1.5, 1.5))
C' = Rotate(C, w, (1.5, 1.5))
D' = Rotate(D, w, (1.5, 1.5))
E' = Rotate(E, w, (1.5, 1.5))
F' = Rotate(F, w, (1.5, 1.5))
G' = Rotate(G, w, (1.5, 1.5))
H' = Rotate(H, w, (1.5, 1.5))
I' = Rotate(I, w, (1.5, 1.5))
J' = Rotate(J, w, (1.5, 1.5))
Vieleck1', a', b', c', d', e', f', g', h', i', j' = Polygon(A', B', C', D', E', F', G', H', I', J')
K = (1, 2)
L = (-1.5, 6)
B_2 = (-1.5, 1)
L' = Rotate(L, 270*°, (1.5, 1.5))
C_2 = Rotate(B_2, 270*°, (1.5, 1.5))
L'_1 = Rotate(L, 180*°, (1.5, 1.5))
D_2 = Rotate(B_2, 180*°, (1.5, 1.5))
L'_2 = Rotate(L, 90*°, (1.5, 1.5))
E_2 = Rotate(B_2, 90*°, (1.5, 1.5))
F_2 = Midpoint(A, E)
s = Segment(A, E)
k_1 = Segment(B, F)
s_4 = Segment(I, D)
Liste1 = Rotate({s, s_4, k_1}, 270*°, (1.5, 1.5))
Liste2 = Rotate({s, s_4, k_1}, 180*°, (1.5, 1.5))
Liste3 = Rotate({s, s_4, k_1}, 90*°, (1.5, 1.5))