  We investigate the nuclear pasta phases in neutron star crusts by conducting
a large number of three-dimensional Hartree-Fock+BCS calculations at densities
leading to the crust-core transition. We survey the shape parameter space of
pasta at constant pressure. Spaghetti, waffles, lasagna, bi-continuous phases
and cylindrical holes occupy local minima in the resulting Gibbs energy
surfaces. The bi-continuous phase, in which both the neutron gas and nuclear
matter extend continuously in all dimensions and therefore protons are
delocalized, appears over a large range of depths. Our results support the idea
that nuclear pasta is a glassy system. Multiple pasta configurations coexist in
a given layer of the crust. At a characteristic temperature, of order
$10^8$-$10^9$K, different phases become frozen into domains whose sizes we
estimate to be 1-50 times the lattice spacing and over which the local density
and electron fraction can vary. Above this temperature, there is very little
long-range order and matter is an amorphous solid. Electron scattering off
domain boundaries may contribute to the disorder resistivity of the pasta
phases. Annealing of the domains may occur during cooling; repopulating of
local minima during crustal heating might lead to temperature dependent
transport properties in the deep layers of the crust. We identify 4 distinct
regions: (1) nuclear pasta first appears as a local minima, but spherical
nuclei are the ground state; (2) nuclear pasta become the absolute minimum, but
spherical nuclei are still a local minimum (3) only nuclear pasta appears in
local minima, and protons are still localized in at least one dimension (4)
only pasta appears, and protons are delocalized. The whole pasta region can
occupy up to 70% of the crust by mass and 40% by thickness, and the layer in
which protons are delocalized could occupy 45% of the crust mass and 25% of its
thickness.
