A description is given of a three-dimensional box-shaped graphene (BSG) nanostructure formed/uncovered by mechanical cleavage of highly oriented pyrolytic graphite (HOPG). The discovered nanostructure is a multilayer system of parallel hollow channels located along the surface and having quadrangular cross-section. The thickness of the channel walls/facets is approximately equal to 1 nm. The typical width of channel facets makes about 25 nm, the channel length is 390 nm and more. The investigation of the found nanostructure by means of a scanning tunneling microscope (STM) allows us to draw a conclusion that it is possible to make spatial constructions of graphene similar to the discovered one by mechanical compression, bending, splitting, and shifting graphite surface layers. The distinctive features of such constructions are the following: simplicity of the preparation method, small contact area between graphene planes and a substrate, large surface area, nanometer cross-sectional sizes of the channels, large aspect ratio. Potential fields of application include: ultra-sensitive detectors, high-performance catalytic cells, nanochannels for DNA manipulation, nanomechanical resonators, electron multiplication channels, high-capacity sorbents for hydrogen storage. (C) 2015 Elsevier B.V. All rights reserved.