A fuel rack for storing nuclear fuel in a fuel pool in one embodiment comprises a baseplate configured for placement in a fuel pool, and a cellular body coupled to the baseplate. The body comprises tightly-packed upwardly open cells which each hold a nuclear fuel assembly. In one embodiment, each cell may have a hexagonal cross-sectional configuration. The cells are each formed by angled cell walls and corners formed between adjoining cell walls. Adjacent cells are arranged to meet in corner-to-corner alignment. This produces triangular-shaped flux traps interspersed between the cells for reactivity control. In some embodiments, at least one peripheral side of the fuel rack has an undulating configuration defining a series of alternating peaks and valleys which nests with a complementary configured peripheral side of an adjacent fuel rack. This provides higher packing density of fuel racks and fuel assemblies in the fuel pool.