Isosceles set $i(9)$
The size of the largest set of points in $\mathbb{R}^{9}$ in which every three points form an isosceles triangle.
Lower bound:
$46$
Verified
(not in the literature)
Upper bound:
$55$
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.
-
Lower bound:
$46$
Checked construction
isosceles-set-9-lower-46, submitted by daniel-munro, 2026-11-05 - Upper bound: None yet
Updates from the literature
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1984
Upper bound: $55$
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.]