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We present results of the application of the numerical continuation andbifurcation package pde2path to the 3D Brusselator model, focusing on snakingbranches of planar fronts between body centered cubes (BCCs) and the spatialhomogeneous solution, and on planar fronts between BCCs and tubes (also calledsquare prisms). These solutions also yield approximations of localized BCCs,and of BCCs embedded in a background of tubes (or vice versa). Additionally, wecompute some moving fronts between lamellas and tubes. To give some theoreticalbackground, and to aid the numerics for the full system, we use the Maxwellpoints for the cubic amplitude system over the BCC lattice.

Snaking branches of planar BCC fronts in the 3D Brusselator