Joint work with István PROK and Jenő SZIRMAI.

The famous Gieseking ideal simplex manifold and the double-simplex manifold, found by I. PROK with his computer program, can be described in Poincaré half-space model of H^3 and by the complex projective line C∞. The Dehn type surgery leads to compact manifolds and cone manifolds (especially orbifolds) through complex 2×2 matrix algebra and attractive pictures.