Patch P3 and P4 successfully created from P0, with nodeeditor program.
So far, each successive patch has used an additional MoI command / Matrix.

Excel 365 matrix math with numbers is great.
Doing matrix "symbolic" math, like .707*z would require some involved programming... Web searches are not much help.

Decomposing a matrix composed of multiple unknown matrices for revolve and mirror is not so easy, and can have multiple, different, correct solutions.
Some mirror mirror ... operations can be done with rotations & ? ... somehow.
Web search results are too simple or too complicated...Some are for elementary school, and some for mathematicians.

Only 8 more patches to figure out...

Edit: Different symmetry operations to create Patch P3 and P4 were created. See post 33.