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{\bf S.J. Cox and E. Flikkema}
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{\bf The Minimal Perimeter for $N$ Confined Deformable Bubbles of Equal Area}
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Candidates to the least perimeter partition of various polygonal
shapes into $N$ planar connected equal-area regions are calculated for
$N\le 42$, compared to partitions of the disc, and discussed in the
context of the energetic groundstate of a two-dimensional monodisperse
foam. The total perimeter and the number of peripheral regions are
presented, and the patterns classified according to the number and
position of the topological defects, that is non-hexagonal regions
(bubbles). The optimal partitions of an equilateral triangle are found
to follow a pattern based on the position of no more than one defect
pair, and this pattern is repeated for many of the candidate
partitions of a hexagon. Partitions of a square and a pentagon show
greater disorder.

Candidates to the least perimeter partition of the surface of the
sphere into $N$ connected equal-area regions are also calculated. For
small $N$ these can be related to simple polyhedra and for $N \ge 14$
they consist of 12 pentagons and $N-12$ hexagons.

\bye
