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Isoptic surfaces of polyhedra

Géza Csima
Jen˝o Szirmai
Journal / Anthology

Computer Aided Geometric Design
Year: 2016
Volume: 47
Page range: 55-60

The theory of the isoptic curves is widely studied in the Euclidean plane E2(see Cie´slak et al., 1991and Wieleitner, 1908and the references given there). The analogous question was investigated by the authors in the hyperbolic H2and elliptic E2planes (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 En(n ≥3)which is called isoptic hypersurface. Now we develope an algorithm to determine the isoptic surface HPof 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.

*Applied Mathematics > Computer Science
*Mathematics > Geometry