Lollipop

There are 1 ~ 8 axes that can flip around. Each piece on the disk is flipped by a subset of axes. All the pieces that correspond to all possible subsets can be found on the disk. In this sense, the puzzle has a complete collection of all possible pieces.
Different rings on the disk contain pieces that are flipped by different types of axes. For example:
- The outmost ring never moves or flips.
- Each piece in the second ring can be flipped by one axis.
- Each piece in the third ring can be flipped by two adjacent axes.
- ... ... ...
- The smallest ring around the core can be flipped by all but one axes.
- The core can be flipped all the axes.

Click the disk to flip.
Drag the disk to rotate the whole disk.
In the batch input box, enter an algorithm and click "Execute" to run it. Any character that is not a number or "L" "R" "l" "r" will be ignored.
Shift + click a ring to magnify it. Shift + click a blank space to reset this effect.

This puzzle is inspired by Complex 3x3x3 and related puzzles, which were proposed and discussed on the Twistypuzzles.com forum. The main contributers are Matt Galla, Carl Hoff, Andreas Nortmann, and others. Related posts include this, this, and this.
The 8-axis puzzle is configured by Brandon Enright. Without his enthusiasm this humongous puzzle will never be constructed.
The puzzle uses html5 canvas, which is not supported directly by IE 8 or lower. Try using the latest version of Chrome for the best experience.