  We present a stochastic algorithm for constructing a topologically disordered
(i.e., non-regular) spatial lattice with nodes of constant coordination number,
the CC lattice. The construction procedure dramatically improves on an earlier
proposal [Phys. Rev. E. 97, 022144 (2018)] with respect to both computational
complexity and finite-size scaling properties - making the CC lattice an
alternative to proximity graphs which, especially in higher dimensions, is
significantly faster to build. Among other applications, physical systems such
as certain amorphous materials with low concentration of coordination defects
are an important example of disordered, constant-coordination lattices in
nature. As a concrete application, we characterize the criticality of the 3D
Ising model on the CC lattice. We find that its phase transition belongs to the
clean Ising universality class, establishing that the disorder present in the
CC lattice is a non-relevant perturbation in the sense of renormalization group
theory.
