I was just wondering if there is a recognised way of referring to all the layers on one side of a puzzle. On a 7x7x7 for example if you turned the right face then you are only turning the outmost layer. What would you call the three layers collectively? Sure I can use common sense but wondered if there was a recognised term. I don't really want the speedcubing notation for a particular side because I need it generically for different puzzles and different sides.

WCA for Cubes up to 5x5x5. SiGN is more general. I can live with both, but I find it important that somebody using a certain notation states which it is. E.g. the turn "u" is something different performed on a 4x4x4. u in WCA is the inner layer under face U turned clockwise as U would turn, in SiGN u means both layers U and the next under it are turned clockwise.