Let l_1,l_2,...,l_7 be mutually different seven lines on the real projective plane. We consider two conditions;(A) No three of l_1,l_2,...,l_7 intersect at a point. (B) There is no conic tangent to any six of l_1,l_2,...l_7. Cummings [3] and White [16] showed that there are eleven non-equivalent classes of systems of seven lines with condition (A)(cf.[7],Chap.18). The purposes of this article is to give an interpretation of the classification of Cummings and White in terms of the root system of type E_7. To accomplish this, it is better to add condition (B) for systems of seven lines. Moreover we need the notion of tetrahedral sets which consist of ten roots modulo signs in the root system of type E_7 and which plays an important role in our study.
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