Abstract
Abstract A p-set of equiangular lines in ℂ3 is a set of p lines spanning ℂ3 each pair of which has the same nonzero angle arccos c, where 0 < c < 1. It is known that via a real matrix representation, a pair of lines in ℝ3 with angle arccos c yields a pair of isoclinic planes in ℝ6 with angle arccos c. In this article we characterize all p-tuples of equi-isoclinic planes in ℝ6 which come via our real matrix representation from p-tuples of equiangular lines in ℂ3. More precisely, we describe quadruples, quintuples up to nine-tuples of equiangular lines in ℂ3.
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