I haven't been able to find the parametric equations and specifications to form a triskelion, a triple spiral (this is made of three interlocked couples of spirals).
Using the parametric equation of an Archimedean spiral, I have tried this (in Matlab):
% Centers of spirals
theta = [0:360*3] * pi / 180; r = theta;
x = r .* cos(theta); y = r .* sin(theta);
theta = [90:120:360] * pi / 180;
xy(:, 1) = cos(theta) * 2 * x(end) / sqrt(3);
xy(:, 2) = sin(theta) * 2 * x(end) / sqrt(3);
% First spiral of first couple
theta = [0:(360*3-60)] * pi / 180; r = theta;
x11 = r .* cos(theta); y11 = r .* sin(theta);
plot(x11 + xy(1, 1), y11 + xy(1, 2))
hold on
% Second spiral of first couple
theta = [0:(360*3+60)] * pi / 180; r = theta;
x21 = r .* cos(theta); y21 = r .* sin(theta);
plot(-x21 + xy(1, 1), -y21 + xy(1, 2))
% First spiral of second couple
theta = [0:(360*3)] * pi / 180; r = theta;
x12 = r .* cos(theta); y12 = r .* sin(theta);
plot(x12 + xy(2, 1), y12 + xy(2, 2))
% Second spiral of second couple
theta = [0:(360*3-120)] * pi / 180; r = theta;
x22 = r .* cos(theta); y22 = r .* sin(theta);
plot(-x22 + xy(2, 1), -y22 + xy(2, 2))
% First spiral of third couple
theta = [0:(360*3+120)] * pi / 180; r = theta;
x13 = r .* cos(theta); y13 = r .* sin(theta);
plot(x13 + xy(3, 1), y13 + xy(3, 2))
% Second spiral of third couple
theta = [0:(360*3)] * pi / 180; r = theta;
x23 = r .* cos(theta); y23 = r .* sin(theta);
plot(-x23 + xy(3, 1), -y23 + xy(3, 2))
axis equal, axis off
As you see it cannot work, only two spirals are interlocked (by construction).
How should the spirals be in order to obtain a nice triskelion?