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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
. Further the
-subcone which is governed by the group
will be discussed for d = 6.
![{\cal G}_{E_6^*}](http://journals.iucr.org/a/issues/2019/03/00/ae5048//teximages/ae5048fi1.gif)
![\Sigma_{d+1 \choose 2}\](http://journals.iucr.org/a/issues/2019/03/00/ae5048//teximages/ae5048fi2.gif)
![{\cal G}_{A_d^*}](http://journals.iucr.org/a/issues/2019/03/00/ae5048//teximages/ae5048fi3.gif)