Limits RegistryPUBLIC RECORD
Limits RegistryDenis Weaire and Robert Phelan, physicists at Trinity College Dublin, found in 1993 a structure using two different cell shapes (irregular pentagonal dodecahedra and tetrakaidecahedra) that partitions space using approximately 0.3% less surface area per cell than Lord Kelvin's 1887 proposed optimal structure, disproving Kelvin's century-old conjecture. The Weaire-Phelan structure remains the best known partition of space by equal-volume cells, though it has not been proven optimal.
The question, scope, and sources behind this Registry record.
Denis Weaire and Robert Phelan, physicists at Trinity College Dublin, found in 1993 a structure using two different cell shapes (irregular pentagonal dodecahedra and tetrakaidecahedra) that partitions space using approximately 0.3% less surface area per cell than Lord Kelvin's 1887 proposed optimal structure, disproving Kelvin's century-old conjecture. The Weaire-Phelan structure remains the best known partition of space by equal-volume cells, though it has not been proven optimal.
There exists a partition of three-dimensional space into equal-volume cells with lower average surface area per cell than Lord Kelvin's 1887 tetrakaidecahedron ('Kelvin structure') partition, disproving Kelvin's conjecture that his structure was optimal.
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
This record has no editable parameters. Read the formal question and assumptions before challenging it.
Current frontiers derived from accepted Claims.
An observed or demonstrated result; no opposing bound is implied.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
1 accepted Claim, with 1 linked evidence records.
Permanent ID limitsregistry.com/limits/LR-WEAIRE-PHELAN-STRUCTURE
No active verified bounties are linked to this Limit.
View verified bounty tracker ↗No accepted machine-checked reproductions are recorded for this Limit.
Limits Registry. LR-WEAIRE-PHELAN-STRUCTURE. Weaire-Phelan structure disproves Kelvin's conjecture. 2026.