regular octagon
a + (sqrt(2) - 2) (x + y)>=0 and sqrt(2) a + a>=2 y and -2 (sqrt(2) - 1) (x - y)<=sqrt(2) a and sqrt(2) a + a + 2 x>=0 and -2 (sqrt(2) - 1) (x + y)<=sqrt(2) a and sqrt(2) a + a + 2 y>=0 and a + (sqrt(2) - 2) (x - y)>=0 and sqrt(2) a + a>=2 x
(1/2 cot(π/8) a, a/2) | (a/2, 1/2 cot(π/8) a) | (-a/2, 1/2 cot(π/8) a) | (-1/2 cot(π/8) a, a/2) | (-1/2 cot(π/8) a, -a/2) | (-a/2, -1/2 cot(π/8) a) | (a/2, -1/2 cot(π/8) a) | (1/2 cot(π/8) a, -a/2)
8
a>0
sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | sqrt(2 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | (1 + sqrt(2)) a | sqrt(2 (2 + sqrt(2))) a | sqrt(2 (2 + sqrt(2))) a | sqrt(2 (2 + sqrt(2))) a | sqrt(2 (2 + sqrt(2))) a
r = 1/2 (1 + sqrt(2)) a
h = 1/2 (-1 - sqrt(2) + sqrt(2 (2 + sqrt(2)))) a
A = 2 (1 + sqrt(2)) a^2
x^_ = (0, 0)
J_x invisible comma x = 1/12 (11 + 8 sqrt(2)) a^4
J_y invisible comma y = 1/12 (11 + 8 sqrt(2)) a^4
J_zz = 1/6 (11 + 8 sqrt(2)) a^4
J_x invisible comma y = 0
r_x = 1/2 sqrt(5/6 + 1/sqrt(2)) a r_y = 1/2 sqrt(5/6 + 1/sqrt(2)) a
a | a | a | a | a | a | a | a
p = 8 a
r = 1/2 (1 + sqrt(2)) a
R = 1/2 sqrt(4 + 2 sqrt(2)) a
sqrt(2 (2 + sqrt(2))) a
χ = 1
A^_ = ((201 + 149 sqrt(2)) a^2)/1152
