Classification of equiangular lines with fixed angle $\arccos(1/(1+2\sqrt2))$

We determine the maximum number $N_{α} (d)$ of equiangular lines with fixed angle $\arccos α$ for $α = 1 / (1 + 2 \sqrt{2})$ in $d$ -dimensional Euclidean space: $2, 3, 4, 6, 8, 10, 14, 15, 16, 17, 18, 20, 22$ for $d \in {2, \dots, 14}$ , and $\max (24, ⌊ 3 (d - 1) / 2 ⌋)$ for $d \geq 15$ . This appears to be the first complete determination of $N_{α} (d)$ in all dimensions $d$ for a fixed nontrivial $α$ , since the work of Lemmens and Seidel for $α = 1 / 3$ in 1973.

Classification of equiangular lines with fixed angle $\arccos (1 / (1 + 2 \sqrt{2}))$

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Classification of equiangular lines with fixed angle $\arccos (1 / (1 + 2 \sqrt{2}))$

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Classification of equiangular lines with fixed angle arccos⁡(1/(1+22))arccos(1/(1+22​))

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Classification of equiangular lines with fixed angle arccos⁡(1/(1+22))arccos(1/(1+22​))

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Classification of equiangular lines with fixed angle $\arccos (1 / (1 + 2 \sqrt{2}))$

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Classification of equiangular lines with fixed angle $\arccos (1 / (1 + 2 \sqrt{2}))$

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