A brane tiling is a bicolored graph on an oriented real 2torus, which conjecturally describes both the derived category of coherent sheaves on a 2dimensional toric Fano stack and the derived category of the directed Fukaya category of the mirror. When the toric Fano stack is the projective plane, the corresponding brane tiling divides the torus into three hexagons. In the talk, based on a joint work in progress with Masahiro Futaki, I will describe the analogue of brane tiling for the projective space, which divides the real 3torus into four truncated octahedra, and explain how it helps to study a torus-equivariant version of homological mirror symmetry.