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The cone of positive-definite quadratic forms is subdivided into aggregates of parallelohedra having certain properties. In E6, the Σ-subcones are investigated and, in particular, the Σ0-subcone will be described which first occurs in E6 and which is governed by the group {\cal G}_{E_6^*}. Further the \Sigma_{d+1 \choose 2}\-subcone which is governed by the group {\cal G}_{A_d^*} will be discussed for d = 6.

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