The terms superhard and ultra-incompressible are commonly used to describe a material's hardness and compressibility approaching the properties of diamond, the hardest and most incompressible single-phase material known so far. Superhard and ultra-incompressible materials are of great interest for applications as well as for basic research. The materials are widely used in various industrial applications, e.g., such as cutting tools or wear-resistant coatings. Basic research focuses on the understanding of structure-property relationships, which yields hints for the design of new superhard and ultra-incompressible materials. Attempts to synthesize or theoretically predict new superhard and ultraincompressible materials are the subject of intensive current research activities. Experimentally accessible and predicted single-phase materials can be classified into three groups: [1] i) crystalline and disordered carbon modifications, ii) compounds formed by the light elements B, C, N, O, and Si, and iii) compounds of transition metals (TMs) with light elements B, C, N, or O. As another more recently developed group of superhard materials, the nanocomposites as multiphase materials have to be mentioned. Most of the materials of classes (i) and (ii) have to be synthesized under extreme conditions. Although these processes are difficult and expensive, materials of these classes have become the most used hard materials for applications (like c-BN and synthetic diamond). The third class of compounds, especially TM carbides and borides, can be synthesized in a comparably facile way at ambient pressure in an arc furnace. Two design parameters are of importance for the selection of superhard or ultra-incompressible TM compounds, [2] i.e., a high electron concentration (EC, electrons per atomic volume) of the TM and the presence of directional covalent bonding. High ECs can be found among the heavy TMs, whereas carbon and boron form short covalent bonds. Among the TMs, 5d metals of groups 6-9, i.e., W, Re, Os, and Ir are the most promising candidates as they show the highest ECs, small atomic volume, and high bulk modulus. Very recently, the properties of several TM borides with high hardness and bulk modulus were studied experimentally and theoretically. [3][4][5][6][7] ReB 2 and OsB 2 were found to be superhard and ultra-incompressible, while OsB was predicted to be ultra-incompressible.In this study, we will focus on boron-rich compounds of the systems Ru-B, Os-B, and W-B. These systems have been investigated for several decades, [7][8][9][10][11]