3D crystals assembled entirely from DNA provide a route to design materials on a molecular level and to arrange guest particles in predefined lattices. This requires design schemes that provide high rigidity and sufficiently large open guest space. A DNA‐origami‐based “tensegrity triangle” structure that assembles into a 3D rhombohedral crystalline lattice with an open structure in which 90% of the volume is empty space is presented here. Site‐specific placement of gold nanoparticles within the lattice demonstrates that these crystals are spacious enough to efficiently host 20 nm particles in a cavity size of 1.83 × 105 nm3, which would also suffice to accommodate ribosome‐sized macromolecules. The accurate assembly of the DNA origami lattice itself, as well as the precise incorporation of gold particles, is validated by electron microscopy and small‐angle X‐ray scattering experiments. The results show that it is possible to create DNA building blocks that assemble into lattices with customized geometry. Site‐specific hosting of nano objects in the optically transparent DNA lattice sets the stage for metamaterial and structural biology applications. A DNA‐origami‐based triangle structure assembles into a 3D rhombohedral crystalline lattice. The accurate assembly of the DNA origami lattice itself as well as the precise incorporation of gold particles is demonstrated by electron microscopy and small‐angle X‐ray scattering experiments.