Glome

A glome, also known as a 3-sphere, is the set of all points in 4D space that are a certain distance away from a given point. This distance is known as the radius. While a glome can be thought of as a limit polychoron with infinitely many cells, glomes themselves are not considered to be polychora.

It is the higher-dimensional analogue of the circle and the sphere.

Any section of a glome with a 3-plane that intersects it is a sphere, and any section with a 2-plane that intersects it is a circle. Sections through the center of the glome are known as great spheres and great circles, respectively.

Vertex Coordinates
The glome is the set of all points (x,y,z,w) such that

$$x^2 + y^2 + z^2 + w^2 = r^2$$

where r is the radius of the glome.