Quadratic forms corresponding to the faces of the Voronoi domain of perfect form in six variables

The problem of classifying integer quadratic forms has a long history, during which many mathematicians have contributed to its solution. Binary forms were comprehensively studied by Gauss. He and later researchers also outlined the main ways to solve the problem of classifying ternary forms and forms of higher dimensions. The greatest achievements of the subsequent period were the deep development of the theory of rational quadratic forms and the complete classification of indefinite forms in dimensions 3 and higher by Eichler in terms of spinor genera.
The paper proposes an algorithm for calculating non-equivalent quadratic forms corresponding to the faces of the Voronoi domain of the second perfect form in many variables, and using this algorithm, all corresponding non-equivalent quadratic forms are calculated.