An octant of a sphere

In geometry, an octant of a sphere is a spherical triangle with three right angles and three right sides. It is one face of a spherical octahedron.

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.^[1]

The octant can be parametrized using a rational quartic Bézier triangle.^[2]

Notes