Pöördsümmeetria

Pöördsümmeetria refers to a type of symmetry in geometry where an object is invariant under a rotation followed by a reflection. This transformation is also known as a rotary reflection. A common example of pöördsümmeetria is found in everyday objects like screws or propellers, where a rotation around an axis and a simultaneous translation along that axis result in the same shape. In more formal mathematical terms, a pöördsümmeetria operation can be represented by a rotation matrix combined with a reflection matrix. The resulting transformation preserves distances and angles, meaning the object looks identical before and after the operation, though its orientation in space might be different. This symmetry element is often denoted by the symbol S_n, where 'n' indicates the order of the rotary reflection, meaning 'n' such operations are required to return the object to its original position. For instance, S_1 represents simple inversion through a point, and S_2 is equivalent to a plane reflection. Objects exhibiting pöördsümmeetria are not always chiral, depending on the specific order 'n'.