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Caption: Mathematical Models by Arnold Emch - Series 2 (1923)
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into six couples (A, A * ) with the following property: A * which lies on S and S* is obtained as the projection from 0 upon Q of a point A which lies on S. But since A * also lies on S, it is obviously projected into the point A upon S*.. T h e projection of the couple {A, A * ) from 0 upon the plane of Sf will therefore give a double point of S'. A s there are six such couples, S', in general, has 6 double points and is of genus 1 0 — 6 = 4. W h e n the quadric Q touches the cubic C in one, two, three, or four points, the n u m b e r of double points will be increased accordingly, so that w e get plane sextics S' with 7, 8, 9, 10 double points, or of genus 3, 2, 1, 0 respectively. T h e models listed below show sextics of genus 4, drawn on transparent glass spheres.1 Fig. 4 ^ n the models the lines run smoothly and evenly. Refraction and reflexion of light mar the effect on the photographs and are the cause of irregularities. [9]
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