Coxeter groups: reflections, rotations

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Page 3 of 4

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Covers angular momentum in rotations, including preservation of angles and vector products.

Covers the concept of 2D rotations and their analytical expressions.

Delves into the symmetries of regular polygons, including the dihedral group and left cosets in a finite group.

Explores the normalization of the product of 4 plane reflections in space.

Explores representation theory and character theory of finite groups, including scalar product and McKay graph.

Covers the concept of orientation in the plane and transformations using matrices.

Covers the rotation between Cartesian frames and their properties in SO(3) and Euler parameterization.

Explores changing bases for rotations, orthogonal planes, and vector transformations under rotation.

Explores isometries in space, transformations preserving lengths and angles, including reflections, rotations, and translations.