On two special classes of parallelohedra in E6

Engel, P.

doi:10.1107/S2053273319001359

On two special classes of parallelohedra in E⁶

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.

Keywords: translation lattices; parallelohedra; cone of positive quadratic forms; Σ-subcones.

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On two special classes of parallelohedra in E6

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On two special classes of parallelohedra in E⁶