This appendix presents the irreducible representations, character tables, and magnetic basis vectors for the hyperhoneycomb lattice in for magnetic field applied parallel and perpendicular to the orthorhombic crystal axes . These are used in the discussion of the calculated magnetic phase diagrams in Sectionย 5.7, especially in regards to Figureย 5.11. In all tables, a primed symmetry operation corresponds to the unprimed symmetry operation followed by time-reversal. For example denotes a 2-fold rotation around followed by time-reversal. All coordinated are in orthorhombic setting with origin choice at .