What is the name of a solid enclosed by four planes and a spherical surface?

Question

I am in the process of writing a paper I ran into a solid that I have no name for. This solid is the volume enclosed by four planes and a spherical surface. The four planes intersect at the sphere center and the arcs created by the intersection between the sphere and the planes are great circle segments. It looks like a pyramid with a rounded base, but I am wondering if there is a formal name.

The edges of the solid are shown in blue. Vertices are shown as blue circles, not including the sphere center.

Answer 1

I suppose you might call it a "solid angle", or even a "rectangular solid angle". Properly speaking, in at least one definition, a solid angle is a measurable subset of the unit sphere, but this is just the cone on that object from the sphere-center, and I doubt anyone would strenuously object.

You could also, I guess, call it a 3D pie-slice.

I look forward to seeing whether there is a more formal name for this particular object.

Answer 2

In Spherical Trigonometry also (3 planes) for instance.. while deriving Sine/Cosine rules no name is given to this solid being talked about. Or at least one that stuck in usage.. High time for coining a new word.

Answer 3

The formal name is spherical pyramid, dated back to $19^{th}$ century.

Quoting from page 186 of Elements of geometry and trigonometry Legendre, A.M. (Adrian Marie) (an online copy of English translation of the book by Charles Davies can be found here)

A spherical pyramid is a portion of the solid sphere, included between the planes of a solid angle whose vertex is the center. The base of the pyramid is the spherical polygon intercepted by the same planes.

Another quote from Elements of Geometry and Trigonometry: From the Works of A. M. Legendre (1867) (this is from google book search)

A Spherical Pyramid is a portion of a sphere bounded by a spherical polygon and sectors of circles whose common center is the center of the sphere.

The spherical polygon is called the base of the pyramid, and the center of the sphere is called the vertex of the pyramid.