Octant of a sphere - Wikiwand
In geometry, an octant of a sphere is a spherical triangle with three right angles and three right sides. It is sometimes called a trirectangular (spherical) triangle.[1] It is one face of a spherical octahedron.[2]
For a sphere embedded in three-dimensional Euclidean space, the vectors from the sphere's center to each vertex of an octant are the basis vectors of a Cartesian coordinate system relative to which the sphere is a unit sphere. The spherical octant itself is the intersection of the sphere with one octant of space.
Uniquely among spherical triangles, the octant is its own polar triangle.[3]
The octant can be parametrized using a rational quartic Bézier triangle.[4]
The solid angle subtended by a spherical octant is π/2 steradian or one-eight of a spat, the solid angle of a full sphere.[5]