A simple trick to design your own solutions for Rubik's cubes

The vast majority of people who tackle the Rubik's cube never succeed in solving it without looking up somebody else's solution. In this video the Mathologer reveals a simple insight that will enable all those of you who can solve the first layer to design your own full solution for the Rubik's cube, as well as for many other highly symmetric twisty puzzles.
For more details about this really very fundamental idea behind many twisty puzzle solutions have a look at this article by the Mathologer from a couple of years ago http://www.qedcat.com/rubiks_cube/
Googling "commutator, Rubik's cube" will also produce links to a lot of very good articles on this topic.
For a few footnotes you may also want to check out this video on Mathologer 2: https://youtu.be/k3IEpugNfJY
The Rubik's cube animations in this video were produced using the program CubeTwister by Werner Randelshofer: http://www.randelshofer.ch/cubetwister/
Thank you also to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.

Enjoy :)

Видео A simple trick to design your own solutions for Rubik's cubes канала Mathologer