Isosceles set $i(8)$
The size of the largest set of points in $\mathbb{R}^{8}$ in which every three points form an isosceles triangle.
Value: $45$ Verified lower bound
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$45$
Checked construction
isosceles-set-8-lower-45, submitted by daniel-munro, 2026-11-05
[construction from P. Lisoněk, New maximal two-distance sets, Journal of Combinatorial Theory, Series A 77 (1997) 318-338.] - Upper bound: None yet
Updates from the literature
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1984
Upper bound: $45$
A. Blokhuis, Few-distance sets, CWI Tract 7 (1984) 1-70.
[via Y.J. Ionin, Isosceles sets, The Electronic Journal of Combinatorics 16 (2009) R141.] -
1997-02
Lower bound: $45$
P. Lisoněk, New maximal two-distance sets, Journal of Combinatorial Theory, Series A 77 (1997) 318-338.
[via Y.J. Ionin, Isosceles sets, The Electronic Journal of Combinatorics 16 (2009) R141.]