A ground level enhancement (GLE) is a solar event that accelerates ions (mostly protons) to GeV range energies in such great numbers that ground-based detectors, such as neutron monitors, observe their showers in Earth's atmosphere above the Galactic cosmic ray background. GLEs are of practical interest because an enhanced relativistic ion flux poses a hazard to astronauts, air crews, and aircraft electronics, and provides the earliest direct indication of an impending space radiation storm. The giant GLE of 2005 January 20 was the second largest on record (and largest since 1956), with up to 4200% count rate enhancement at sea level. We analyzed data from the Spaceship Earth network, supplemented to comprise 13 polar neutron monitor stations with distinct asymptotic viewing directions and Polar Bare neutron counters at South Pole, to determine the time evolution of the relativistic proton density, energy spectrum, and three-dimensional directional distribution. We identify two energy-dispersive peaks, indicating two solar injections. The relativistic solar protons were initially strongly beamed, with a peak maximum-to-minimum anisotropy ratio over 1000:1. The directional distribution is characterized by an axis of symmetry, determined independently for each minute of data, whose angle from the magnetic field slowly varied from about 60 • to low values and then rose to about 90 • . The extremely high relativistic proton flux from certain directions allowed 10 s tracking of count rates, revealing fluctuations of period 2 minutes with up to 50% fractional changes, which we attribute to fluctuations in the axis of symmetry.