What property of rotation preserves relative position?

Question

simple terminology question here.

What is the property of rotation which causes objects maintain their relative positions between each other in space? I don't suppose it's the fact that it's an affine transformation, but something more specific...

Thanks.

Answer 1

Rotations in $\bf{R^{3}}$ (and $n$-dimensional Euclidean space), are isometries.

http://en.wikipedia.org/wiki/Isometry#Examples