Gear Cube Extreme

Here is another puzzle I have no interest in trying to remember how to solve. Just look at the notes I made when I figured it out years ago, solve it, and put it away. I found my notes in the Solution Guides Pre Fall 2013 document. I'm adding some (hopefully) minor edits to help clarify things if I ever come back to this in the future.

Since the U and D layers on the Extreme can turn 90˚, U means 90˚, but since R can not turn 90˚, R means 180˚.

Middle Layer
The middle layer is never far from solved. Good place to start.

Corners
Super Square 1; Corners First
May 2020 observation: Over the years I have totally neglected the Super Square 1 and have changed the way I do corners with Corners First. So this is not helpful. Well... it kind of is. The Square-1 thing means get all the whites on the bottom. I remember how to do that. The Corners First thing. If there are two pairs, that is easy. I remember that one. If there is one pair, even though I have a new improved method, it won't work with the Gear Extreme because of 90˚ turns, but I remembered the old one pair algorithm.

Centers
Centers haven't had to be solved individually the last few solves, but during the experimentation phase a double swapper was discovered. With yellow up, to swap Top with Bottom, and Front with Back do (RU2) x 6.

Edges—Permutation
You know how M2U2 M2U2 on a cube does a double swap of edges? R2U2 R'2U2 does a double swap without twisting the edges. R2U2 R2U2 does the double swap while twisting edges.

Edge 3-cycle: (UL' U'R UL'x2 U'R' UL U') (U'R UL' U'Rx2 UL U'R' U)
(top back top back top back-2 top forward top forward top) x 2
cycles DR to DL to UB (based on the crazy 332 corner 3-cycle.)

Edges—Orientation
R x 4 twists all 4 M slice edges 2 notches counterclockwise.
(RU) x 12 twists UF, UR, and DR 2 notches counterclockwise.
The above two along with their families can be used to do any flipping that comes up. Even if only one piece needs flipped, some combination of these can do the job.