L
R
B
D

-- v = very wide = whole tetrahedron -- ' = i = counter clockwise --       BETA solver   --  

This is a (not yet existing) edge turning jing pyraminx, with extra corner cuts (to de-bandage). Centers are steady, edges can only twist in place. No jumbling.

Idea: ©Twizzle.net. Tip: test the algorithms on pristine tetrahedron to see their effects, which pieces exchange (and/or twist).