Editing Dihedral angle (section)

==Law of cosines for dihedral angle==
Given 3 faces of a polyhedron which meet at a common vertex P and have edges AP, BP and CP, the cosine of the dihedral angle between the faces containing APC and BPC is:<ref>{{cite web|title=dihedral angle calculator polyhedron|url=http://www.had2know.com/academics/dihedral-angle-calculator-polyhedron.html|website=www.had2know.com|access-date=25 October 2015|archive-url=https://web.archive.org/web/20151125044900/http://www.had2know.com/academics/dihedral-angle-calculator-polyhedron.html|archive-date=25 November 2015|url-status=dead}}</ref>
:<math>\cos\varphi = \frac{ \cos (\angle \mathrm{APB})  - \cos (\angle \mathrm{APC}) \cos (\angle \mathrm{BPC})}{ \sin(\angle \mathrm{APC}) \sin(\angle \mathrm{BPC})}  </math>
This can be deduced from the [[spherical law of cosines]], but can also be found by other means.<ref>{{cite web|title=Formula Derivations from Polyhedra|url=http://www.whistleralley.com/polyhedra/derivations.htm|access-date=4 December 2024}}</ref>