<p>Homogenisation-based topology optimisation offers a computationally efficient approach to inverse design of 3D high-resolution lightweight mechanical structures. By considering a homogenised representation of periodic microstructures the optimisation can be applied on a coarser mesh, and the optimised multi-scale result allows for up-sampling to a single-scale geometry in a post-processing step termed dehomogenisation. Existing methods for performing 3D dehomogenisation are challenged by high computational complexity or, due to their global nature, a lack of robustness with respect to orientation singularity and discontinuity. Phasor noise is a compactly parameterised pattern-generating algorithm that has been proven to offer significant improvements for 2D dehomogenisation in terms of the trade-off between computational efficiency and solution quality. The representation of the design is continuous and periodic at each intermediate step of the dehomogenisation procedure. This maintains the computational advantage of the phasor noise formulation throughout the procedure, as well as ensures a finalised multi-scale design with appropriate length scale and thicknesses. The phasor-based formulation is based on spatial locations and distances, making it inherently mesh-independent. This paper extends the 2D phasor-based dehomogenisation procedure to 3D. Adaptions are required to improve performance for the more general case of 3D optimised results, where ensuring appropriate structural connectivity is especially addressed. Additionally, a novel method for introducing local infill in the dehomogenised design, improving the design process for additive manufacturing further, is presented. The proposed dehomogenisation procedure has been implemented in collaboration with the software company nTopology, using the implicit geometry kernel of the nTop software to exploit the implicit and continuous nature of the phasor noise framework.</p>