Isosceles set $i(6)$

The size of the largest set of points in $\mathbb{R}^{6}$ in which every three points form an isosceles triangle.

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: $28$ Checked construction
  isosceles-set-6-lower-28, submitted by daniel-munro, 2026-11-05
  [construction from Y.J. Ionin, Isosceles sets, The Electronic Journal of Combinatorics 16 (2009) R141.]
• Upper bound: None yet

Updates from the literature

• 1984 Upper bound: $28$
  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.]
• 2009-11-24 Lower bound: $28$
  Y.J. Ionin, Isosceles sets, The Electronic Journal of Combinatorics 16 (2009) R141.
  [via Sequence A175769 in the OEIS]