Near the end of World War I, Georges Vantongerloo felt the need to break with the past. He came in contact with a group of artists, including Theo van Doesburg and Piet Mondrian, who saw abstraction as an almost spiritual vehicle for the reconstruction of art and society. Their approach, known as De Stijl (The Style), was marked by fundamentals: geometry combined with asymmetry; pure primary colors with black and white; and positive and negative elements. Motivated by his belief in this utopian aesthetic, Vantongerloo joined the De Stijl group in 1917, its founding year.

In 1919 he embarked on a series of sculptures based on the interrelation of masses. Interrelation of Volumes from the Ellipsoid, the fifth in the group, explores the intersections of a parallel-faced polyhedron within an ovoid volume. To produce this work, the artist mapped the intersecting volumes of forms from different views in order to reveal core geometric units and planes. While this sculpture was inspired by mathematical principles, it is not a sterile, scientific object but, in its realized form, suggests an element of human invention in the mold marks and alterations that Vantongerloo considered part of the artistic process.