The ditrigonaries share a regiment.
A regiment[1] is a group of polytopes that share edge arrangements. The most convex representative of a regiment is called a colonel, with it's conjugate being called the lieutenant. A regiment is named after it's colonel (for example, the icosahedron regiment is named after the icosahedron because it is the most convex of the members, which consist of the colonel and the great dodecahedron).