The theory of the isoptic curves is widely studied in the Euclidean plane E 2 (see Cieślak et al., 1991 and Wieleitner, 1908 and the references given there). The analogous question was investigated by the authors in the hyperbolic H 2 and elliptic E 2 planes (see Csima and Szirmai, 2010, 2012, submitted for publication), but in the higher dimensional spaces there are only few results in this topic. In Csima and Szirmai (2013) we gave a natural extension of the notion of the isoptic curves to the n-dimensional Euclidean space E n ( n ≥ 3 ) which is called isoptic hypersurface. Now we develope an algorithm to determine the isoptic surface H P of a 3-dimensional polyhedron P . We will determine the isoptic surfaces for Platonic solids and for some semi-regular Archimedean polytopes and visualize them with Wolfram Mathematica (Wolfram Research, Inc., 2015). 
Isoptic surfaces of polyhedra