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The intersection of a quadric and a cubic surface in 3-space is a canonicalcurve of genus 4. It has 120 complex tritangent planes. We present algorithmsfor computing real tritangents, and we study the associated discriminants. Wefocus on space sextics that arise from del Pezzo surfaces of degree one. Theirnumbers of planes that are tangent at three real points vary widely; both 0 and120 are attained. This solves a problem suggested by Arnold Emch in 1928.

Real Space Sextics and their Tritangents