Symmetrical hexaprimas
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Abstract
The principal classes of hexaprimas, or what are commonly called space curves of the 3rd order, were derived by Seidewitz and are given in the well-known manual by Reye under the names 1) space hyperbola, 2) space ellipse, 3) parabolic hyperbola, and 4) space parabola. This note is the result of the question: is it possible to construct a hexaprima possessing symmetry? The term hexaprima denotes a prima of points that is completely and uniquely determined by six points, and a space curve of the 3rd order is precisely such a curve. We obtain three constructions leading to hexaprimas of three types of symmetry (see the article).
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