I will describe the construction of an infinite family of cells called bisimplices and their application to the construction of classifying spaces of quadric groups. The 1-skeleta of these cells are complete bipartite graphs, making them well suited to the construction of higher skeleta of certain families of bipartite graphs. The construction of bisimplices poses special challenges since, unlike simplices and cubes, they cannot be realized as polyhedra. An essential component of the construction is an application of the discrete Morse theory of Forman to the recognition of spheres.