Biflippers and head to tail composition rules

A new graphical calculus for operating with isometries of low dimensional spaces of classical geometries is proposed. It is similar to a well-known graphical representation for vectors and translations in an affine space. Instead of arrows, we use biflippers, which are arrows framed at the end points with subspaces. The head to tail addition of vectors and composition of translations is generalized to head to tail composition rules for isometries.