Friction angle ($\phi =\arctan \mu$)

The limiting angle between a contact resultant and the compressive normal force when static friction obeys $|F_t|\le \mu N$. Resolving the resultant gives $\tan \phi =|F_t|/N$, so admissible contact forces lie within a cone of half-angle $\arctan \mu$ about the inward normal. A contact-force magnitude is generally $\sqrt{N^2+F_t^2}$, distinct from N.

For symmetric upper faces inclined by alpha from the vertical, inward normals push partly downward. Limiting upward friction gives vertical support $2N(\mu \cos \alpha -\sin \alpha )$. Balancing weight yields the displayed minimum normal grip. The corresponding minimum total contact magnitude per face is $N_{\min }\sqrt{1+{\mu }^2}$. It is achieved at the limiting friction angle. The formula assumes symmetric contacts with cancelling horizontal force and torque and positive denominator.