Symmetric Patterns 

With the Symmetry Editor of Cube Explorer you can search for symmetric cube patterns. We will give some explanation concerning the mathematics of such symmetries here. A cube has 48 symmetries which build the symmetry group M with 48 elements. A cube symmetry is a geometric transformation, which maps the cube onto itself. If the cube has a pattern, this pattern usually will not map onto itself too.


Here is a table of the possible 48 symmetries of the cube


There are patterns which only have one of the above symmetries (except the identity), but there also are patterns which have several symmetries. A pattern could be for example symmetric with respect to all three reflections through a plane . This automatically implies the symmetries and . The resulting symmetry type in this example is . An example for a pattern, which has this symmetry is . Altogether there are 33 basically different symmetry types which correspond to certain subgroups of the symmetry group M. 

Look at this table to get more information about the 33 symmetry types and cube patterns with these symmetries. 