A spherical tetrahedron is a three-dimensional simplex in spherical geometry. In the unit hypersphere 
, it is bounded by four geodesic faces,
each of which is a spherical triangle. Its
six edge lengths and six dihedral angles are angular
quantities, and its ambient space has constant curvature
1.
The volume of a spherical tetrahedron may be expressed in terms of either its edge lengths or its dihedral angles (Murakami 2012), and its infinitesimal variation satisfies the Schläfli differential formula. A spherical tetrahedron in this sense should not be confused with the Reuleaux tetrahedron, which is a Euclidean solid bounded by spherical patches.
