High strength, low density columnar structure

A high strength, low density modular columnar structure. In the preferred embodiment, each module is a prism or cuboid having three or four vertical rectangular sides which meet in the module corners. The module ends perpendicular to the sides are the module faces. At least one face has a brace panel. The brace panels and the face are preferably the same shape, but off-set. A plurality of preferably triangular brace arms extends to the module corners. Each brace panel is preferably provided with a centrally located aperture. The lower face of each module is preferably provided with a lip, while the upper face is configured to receive the lip. A cylindrical column extends vertically through the center of each module, and a plurality of struts extends radially from each column. A stack of modules may be secured with a bolt run through the module apertures, an adhesive, or simply gravity.