Abstract: A heat pipe fuel element includes an evaporation section, a condensing section, a capillary section connecting the evaporation section to the condensing section, and a primary coolant. In a cross-section in a plane perpendicular to a longitudinal axis of the evaporation section, the heat pipe fuel element includes a cladding layer enclosing an interior area including a fuel body formed of a fissionable fuel composition and that has an outer surface oriented toward the cladding layer and an inner surface defining a periphery of a vaporization space of the evaporation section. The fuel body has a structure with a shape corresponding to a mathematically-based periodic solid, such as a triply periodic minimal surface (TPMS), and the evaporation sections of a plurality of heat pipe fuel elements are arranged in a phyllotaxis pattern (as seen in a cross-section in a plane perpendicular to a longitudinal axis of the active core region).