MPEJ Volume 6, No. 6, 10 pp.
Received May 28 2000, Revised November 29 2000, Accepted December 6 2000
L. Bowen
Circle Packing in the Hyperbolic Plane
We consider circle packings in the hyperbolic plane, by finitely many
congruent circles, which maximize the number of touching pairs.
We show that such a packing has all of its centers located on the vertices
of a triangulation of the hyperbolic plane by congruent equilateral
triangles, provided the diameter $d$ of the circles is such that an
equilateral triangle in the hyperbolic plane of side length $d$ has each
of its angles is equal to $2\pi /N$ for some $N>6$.