In geometry, an improper rotation (also called rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space...

computer graphics. In some literature, the term rotation is generalized to include improper rotations, characterized by orthogonal matrices with a determinant...

pseudoscalars and pseudotensors, both of which gain an extra sign-flip under improper rotations compared to a true scalar or tensor. Physical examples of pseudovectors...

the transformation. But a (proper) rotation also has to preserve the orientation structure. The "improper rotation" term refers to isometries that reverse...

The improper rotation is represented by the symbol Sn where n is the order. Since the improper rotation is the combination of a proper rotation and a...

see how our definition of improper rotation corresponds with the geometric interpretation: an improper rotation is a rotation around an axis (here, the...

do not form a group because the product of two improper rotations is a proper rotation. The rotation group is a group under function composition (or...

\operatorname {cl} S} . In crystallography, an overline indicates an improper rotation or a negative number: 3 ¯ {\displaystyle {\overline {3}}} is the Hermann–Mauguin...

centers of inversion, C for proper rotation axes, σ for mirror planes, and S for improper rotation axes (rotation-reflection axes). C and S are usually...

has the symmetry of a tetrahedron. Td includes improper rotation operations, T excludes improper rotation operations, and Th is T with the addition of an...