The direct chemical vapour deposition of freestanding graphene gyroids with controlled sub-60 nm unit cell sizes is demonstrated. Three-dimensional (3D) nickel templates were fabricated through electrodeposition into a selectively voided triblock terpolymer. The high temperature instability of sub-micron unit cell structures was effectively addressed through the early introduction of the carbon precursor, which stabilizes the metallized gyroidal templates. The as-grown graphene gyroids are self-supporting and can be transferred onto a variety of substrates. Furthermore, they represent the smallest free standing periodic graphene 3D structures yet produced with a pore size of tens of nm, as analysed by electron microscopy and optical spectroscopy. We discuss generality of our methodology for the synthesis of other types of nanoscale, 3D graphene assemblies, and the transferability of this approach to other 2D materials.