Master of Science / Department of Mathematics / Natasha Rozhkovskaya / “Incomplete open cubes” is one of the major projects of the artist Sol Lewitt. It consists of a collection of frame structures and a presentation of their diagrams. Each structure in the project is a cube with some edges removed so that the structure remains three-dimensional and connected Structures are considered to be identical if one can be transformed into another by a space rotation (but not reflection). The list of incomplete cubes consists of 122 structures. In this project, the concept of incomplete cubes was formulated in the language of graph theory. This allowed us to compare the problem posed by the artist with the similar questions of graph theory considered during the last decades. Classification of Incomplete cubes was then refined using the language of combinatorics. The list produced by the artist was then checked to be complete. And lastly, properties of Incomplete cubes in the list were studied.