Introduction Regular tessellations Finite groups of rotations Groups generated by two or three reflections The Petrie polygon of a tessellation The regular tesselations $\{p,q\}_r$ Three-dimensional honeycombs The simplex, cube, cross polytope and 24-cell The 120-cell and the 600-cell Groups generated by four reflections The Petrie polygon of a honeycomb The regular honeycombs $\{p,q,r\}_t$ Finite groups of quaternions Quaternions and Petrie polygons Table 1. Regular tessellations $\{p,q\}_r$ and their groups Table 2. Reflexible honeycombs and their groups Table 3. Twisted honeycombs and their groups References