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There are investigated supergroups of some hyperbolic space groups with simplicial fundamental domain. If the vertices of these simplices are out of the absolute, we can truncate them by polar planes of the vertices and the new polyhedra are fundamental ones of the richer groups. In papers of E. Molnar, I. Prok and J. Szirmai the simplices, investigated here, are collected in families F3, F4 and F6. We have constructed at least one new hyperbolic space group for each truncated simplex in these families. 2010 Mathematics Subject Classifications. 51M20, 52C22, 20H15, 20F55. .

Fundamental simplices with outer vertices for hyperbolic groups and their group extensions for truncations