gPatchP0_01.3dm is a new network of curves for fundamental gyroid patch P0, via Python math and .css files, without zeta rotation of 45 degrees, and without eta move of n/4. (zeta and eta, greek letters, are defined in Table 1. The typesetter got zeta mixed up with another greek letter.)

GyroidBoundaryFrom_gPatchP0_02_3dm.7z is the nodeeditor program which uses P0 to produce P1 and P2, in MoI, with Table 1 Transformations. (rotate, mirror, move). The node permits quick variations in the +/- rotation degrees, the mirror plane(s), and the move amounts.
Nodes for P3...P12 have not yet been done. The sign of both 45 degree rotations had to be reversed from the angle figured out.

MatrixMultiply4.zip is an Excel 365 program to multipy matrices with number entries, to assist in decomposing each composite matrix for each line entry in Table 1.

Each composite matrix is created manually from the [x, y, z,1] (transposed) vector.
A symbolic matrix multiplier in Excel would be helpful...

- Brian

ps The node program has a macro for the XY plane/frame for mirror can be exported, and a copy placed in the macro folder of nodeeditor.
gPatchP0 network can be networked to a surface. The surface can be offset a little, if desired. The net, or the surface(s) can be input to the node program to yield P1 and P2, etc.

EDIT: Updated .node program and Excel 365 programs are in post 31.