Interesting theme...)) I'll try too, old - but topical...)) Some of my own created origami folding technics :
Extended hex-pleating, (not R.Lang's usual Hex-Pleating) - its other field and grid structures, depends on several parameters HP{a;b;с}, a,b,с - integer, like one of them HP{1;3}:
Or RP - rhombic pleating, all collection RP{a;b}
Like this one RP{2;4}
Usual Octagon Pleating (OP):
My old model in OP{2;3}:
and many, many others in RP{a;b};HP{a;b;c}; OP{a;b;c;d};...;NP{a;...;z} type
something like this DP - decagon pleating, DDP - dodecagon pleating:
et.c.
Or old non-periodic or combined methodic - MP (mix pleating):
In this technics are many math and geometry, but all is easy foldable and usable in experienced hands.
More detailed info may be found at
My Book.
I found also a few collections of really interest origami technics, but i can't tell it now... needed for future publications...
Best Regards from Russia,
Andrey