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arXiv · 2603.02469

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

Theodore Gossett·Zilin Jiang·Adam Teets·Zoe Wellner
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Abstract

We determine the maximum number $N_α(d)$ of equiangular lines with fixed angle $\arccosα$ for $α= 1/(1+2\sqrt2)$ 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 $\max(24, \lfloor 3(d-1)/2 \rfloor)$ for $d \ge 15$. 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.

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Theodore Gossett, Zilin Jiang, Adam Teets, Zoe Wellner. 2026-03-02. Classification of equiangular lines with fixed angle $\arccos(1/(1+2\sqrt2))$. https://arxiv.org/abs/2603.02469

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