  We construct a three-dimensional (3D), time-reversal symmetric generalization
of the Chalker-Coddington network model for the integer quantum Hall
transition. The novel feature of our network model is that in addition to a
weak topological insulator phase already accommodated by the network model
framework in the pre-existing literature, it hosts strong topological insulator
phases as well. We unambiguously demonstrate that strong topological insulator
phases emerge as intermediate phases between a trivial insulator phase and a
weak topological phase. Additionally, we found a non-local transformation that
relates a trivial insulator phase and a weak topological phase in our network
model. Remarkably, strong topological phases are mapped to themselves under
this transformation. We show that upon adding sufficiently strong disorder the
strong topological insulator phases undergo phase transitions into a metallic
phase. We numerically determine the critical exponent of the insulator-metal
transition. Our network model explicitly shows how a semi-classical percolation
picture of topological phase transitions in 2D can be generalized to 3D and
opens up a new venue for studying 3D topological phase transitions.
