Symmetrical hexaprimes

Abstract

The most important categories of hexaprimes, or what is commonly called spatial curves of the 3rd order, were derived by Seydewitz and are given in the famous manual by Reye under the names 1) spatial hyperbola, 2) spatial ellipse, 3) parabolic hyperbola and 4) spatial parabola. This note was the result of a task: is it possible to build a hexaprima that has symmetry? The term hexaprima means such a prima of points that is completely and unambiguously determined by six points, and a 3rd order spatial curve is just such a curve. We get three constructions leading to hexaprimes of three types of symmetry (see article).