  Fracton topological order describes a remarkable phase of matter which can be
characterized by fracton excitations with constrained dynamics and a ground
state degeneracy that increases exponentially with the length of the system on
a three-dimensional torus. However, previous models exhibiting this order
require many-spin interactions which may be very difficult to realize in a real
material or cold atom system. In this work, we present a more physically
realistic model which has the so-called X-cube fracton topological order but
only requires nearest-neighbor two-spin interactions. The model lives on a
three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of
freedom on each site and a unit cell of 6 sites. The model is constructed from
two orthogonal stacks of $Z_2$ topologically ordered Kitaev honeycomb layers,
which are coupled together by a two-spin interaction. It is also shown that a
four-spin interaction can be included to instead stabilize 3+1D $Z_2$
topological order. We also find dual descriptions of four quantum phase
transitions in our model, all of which appear to be discontinuous first order
transitions.
