on a die aaaa rotoreflection aaaa "grouped" group table

* In the study of geometry, one is constantly confronted with groups of
transformations on various "spaces." Many of these groups consist simply
of the symmetries of those spaces with respect to suitably chosen
properties. An obvious example is furnished by the symmetries of the
cube. Geometrically speaking, these are the one-one transformations which
preserve distances on the cube. They are known as "isometries," and are
48 in number. *

[Birkhoff & MacLane, Survey of Modern Algebra (1941), p. 127]
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