Oleg Viro (Stony Brook University) "Generators, relations and head to tail compositions" Any isometry of a non-degenerate inner product space can be presented as a composition of two reflections in subspaces. In low dimensions this provides a convenient graphical encoding of isometries similar to (and, in a sense, generalizing) the encoding of translations by arrows and composition of translations to the head to tail addition of vectors. Non-uniqueness of representation for rotations and translations as compositions by two reflections provides a simple complete system of relations among the reflections. Generalizations to other classical geometries, spin and pin groups also will be discussed