User:Tomruen/Flat toroid polyhedron

=Flat toroid polyhedron= Regular maps of the form {4,4}m,0 can be represented as the finite regular skew polyhedron {4,4 | m}, seen as the square faces of a m×m duoprism in 4-dimensions.

Generators
Group: [4,4], order 4(b2+c2):

Given rotation angles:
 * $$\alpha_1 = 2\pi c / (b^2+c^2)$$
 * $$\alpha_2 = 2\pi b / (b^2+c^2)$$

Generators:
 * $$ \sigma_1 = \left [\begin{smallmatrix}cos(\alpha_1)&-sin(\alpha_1)&0&0\\sin(\alpha_1)&cos(\alpha_1)&0&0\\0&0&cos(\alpha_2)&-sin(\alpha_2)\\0&0&sin(\alpha_2)&cos(\alpha_2)\end{smallmatrix}\right ]$$
 * $$ \sigma_2 = \left [\begin{smallmatrix}cos(\alpha_2)&sin(\alpha_2)&0&0\\-sin(\alpha_2)&cos(\alpha_2)&0&0\\0&0&cos(\alpha_1)&-sin(\alpha_1)\\0&0&sin(\alpha_1)&cos(\alpha_1)\end{smallmatrix}\right ]$$