Octant of a sphere

Short description: Spherical triangle with three right angles

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.

The octant can be parametrized using a rational quartic Bézier triangle.