In cylindrical structures subjected to torsion, maximum compressive and tensile shear strains lie along helices on the surface that form an angle of 45° with the long axis of the cylinder. These two helices intersect at an angle of 90°. The general structure of mammalian skulls approaches one-half of a right circular cylinder, where the flat side represents the palate. As a result of chewing or biting on only one side of the head at a time, the anterior rostral region of many mammalian skulls tends to be twisted relative to the posterior braincase, around an anteroposterior axis. Helices as described above can generally be traced from the braincase to the rostrum on the surface of these skulls.

In many modern selenodont artiodactyls (antelopes, deer, etc.) the postorbital bars contribute to such buttresses: they lie along helices that form an angle of 90° with each other and 45° with the long axis of the skull, modeled as a half cylinder. These helices lie at the surface of the skull as far from the twisting axis as possible for maximum effect, and they connect the braincase and the rostrum by bridging the inherently weak orbital region. A less obvious preorbital tract also meets these requirements.

Torsion in carnivore skulls results when the canine tooth on one side meets resistance while the other encounters soft tissue. Compressive and tensile helices that connect the canine tooth with the opposite jaw joint can be traced on the surface of these skulls. The most efficient connection between the braincase and the anterior region of the skull requires that the ratio between the length and width of the skull be less than or equal to π/2. Carnivore skulls meet these requirements, and in no case is the ratio greater than π/2.