A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without
disturbing other circles of the packing (e.g., Niggli 1927, Niggli 1928, Fejes Tóth
1960/61). Böröczky (1964) exhibited stable systems of congruent unit circles
with density 0. A rigid packing of circles can be obtained from a hexagonal tessellation
by removing the centers of a hexagonal web, then replacing each remaining circle
with three equal inscribed circles (appropriately oriented), as illustrated above
(Meschkowski 1966, Wells 1991).
Böröczky, K. "Über stabile Kreis- und Kugelsysteme." Ann. Univ. Sci. Budapest, Eötvös Sect. Math.7,
79-82, 1964.Fejes Tóth, L. "On the Stability of a Circle
Packing." Ann. Univ. Sci. Budapestinensis, Sect. Math.3-4, 63-66,
1960/1961.Meschkowski, H. Unsolved
and Unsolvable Problems in Geometry. London: Oliver & Boyd, 1966.Niggli,
Z. Z. für Kristallographie65, 391-415, 1927.Niggli,
Z. Z. für Kristallographie68, 404-466, 1928.Wells,
D. The
Penguin Dictionary of Curious and Interesting Geometry. London: Penguin,
pp. 30-31, 1991.
