Anti-rotation coupling for use in a downhole assembly

A downhole assembly that includes tubulars rotationally coupled to one another. An interface is between adjacent tubulars that makes up at least a portion of the rotational coupling. Certain surfaces of adjacent tubulars come into contact with one another when adjacent tubulars are rotationally coupled; and which are defined as contact surfaces. Each contact surface is profiled with facets that are complementary to facets on a corresponding contact surface of an adjacent tubular. The profiling of the contact surfaces is such that when a contact surface is brought together with a corresponding contact surface; facets on the contact surface abut facets on the corresponding contact surface along planes that are oblique or parallel with an axis of the tubular. At least some of a rotational torque transmitted between adjacent tubulars occurs across the abutting facets.