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:(''X''<sup>*</sup>, Δ,''X''<sub>*</sub>, Δ<sup>v</sup>),
where
*''X''<sup>*</sup> and ''X''<sub>*</sub> are free abelian groups of finite [[rank]] together with a perfect pairing between them with values in '''Z''' (in other words, each is identified with the [[dual lattice]] of the other).
*Δ is a finite subset of ''X''<sup>*</sup> and Δ<sup>v</sup> is a finite subset of ''X''<sub>*</sub> and there is a bijection from Δ onto Δ<sup>v</sup>, denoted by α→α<sup>v</sup>.
*For each α, (α, α<sup>v</sup>)=2
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