Abstract:
Davenport had found the first two cubic forms g<sub>1</sub>, g<sub>2</sub>, the meaning of which for ternary forms is the same as the meaning of the Markov forms for binary quadratic forms. Swinnerton-Dyer computed next 18 extremal cubic ternary forms. Klein's polyhedra for the forms g<sub>1</sub>, g<sub>2</sub>, g<sub>3</sub> were computed in [14-17]. In all these cases each face has no more then 5 integer points. In this paper the form g with 28 interior points on a face have studied. Its symmetry group and other properties are studied as well. There is a cubic field, which corresponds to these polyhedra. The vector of this field is expanded by some multidimensional generalization of continued fractions algorithm. The integer convergents of these continued fractions are concerned with respect to the Klein polyhedra.
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