Abstract
It is proposed that certain non-crystallographic polyhedral clusters, which are not able to grow, possess the potential to bifurcate, regroup and self-replicate. Conditions under which this self-replicating growth mechanism may become favoured energetically over normal crystal growth are stated. The basic idea is illustrated by some polyhedral structural models related to those designed for the solution of the structure of the clay mineral allophane, an alumino-silicate analog of the spheroidal fullerenes.
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