Isometry group

Imagine you're playing with your toy blocks. If you try to move the blocks around, you might notice that some arrangements look the same as other arrangements even though the blocks are in different spots.

The isometry group is like a rule book that helps us understand what arrangements of blocks are the same. It tells us all the different ways we can move the blocks around without changing the overall shape or size of the group of blocks. These movements are called "isometries."

For example, if we have a square arrangement of blocks, we can spin the square around or flip it over and get the exact same square. We could also slide it to the left or right, but if we slide it too far, it won't be the same square anymore.

The isometry group helps us understand all of these different movements we can make without changing the shape or size of the group of blocks. It's like a map that shows us all the allowable routes we can take while playing with our blocks.