Volume and Boundary Face Area of a Regular Tetrahedron in a Constant Curvature Space
arXiv:1803.10809
Abstract
An example of the volume and boundary face area of a curved polyhedron for the case of regular spherical and hyperbolic tetrahedron is discussed. An exact formula is explicitly derived as a function of the scalar curvature and the edge length. This work can be used in loop quantum gravity and Regge calculus in the context of a non-vanishing cosmological constant.
18 pages, 6 figures, 3 appendices