  The first results of a new three-dimensional, finite temperature
Skyrme-Hartree-Fock+BCS study of the properties of inhomogeneous nuclear matter
at densities and temperatures leading to the transition to uniform nuclear
matter are presented. Calculations are carried out in a cubic box representing
a unit cell of the locally periodic structure of the matter. A constraint is
placed on the two independent components of the quadrupole moment of the
neutron density in order to investigate the dependence of the total
energy-density of matter on the geometry of the nuclear structure in the unit
cell. This approach allows self-consistent modeling of effects such as (i)
neutron drip, resulting in a neutron gas external to the nuclear structure,
(ii) shell effects of bound and unbound nucleons, (iii) the variety of exotic
nuclear shapes that emerge, collectively termed `nuclear pasta' and (iv) the
dissolution of these structures into uniform nuclear matter as density and/or
temperature increase. In part I of this work the calculation of the properties
of inhomogeneous nuclear matter in the core collapse of massive stars is
reported. Calculations are performed at baryon number densities of $n_{\rm b}$
= 0.04 - 0.12 fm$^{\rm -3}$, a proton fraction of $y_{\rm p}=0.3$ and
temperatures in the range 0 - 7.5 MeV. A wide variety of nuclear shapes are
shown to emerge. It is suggested that thermodynamical properties change
smoothly in the pasta regime up to the transition to uniform matter; at that
transition, thermodynamic properties of the matter vary discontinuously.
