hypercuboids

Example:While a hypercuboid is defined by its rectangular faces, a hypersphere is defined by all points at a fixed distance from the center.

Definition:In higher-dimensional geometry, a hypersphere is the analog of a sphere in n-dimensional space, which is fundamentally different from a hypercuboid.

Example:A hyperplane divides an n-dimensional space into two regions, whereas a hypercuboid defines regions by rectangular boundaries.

Definition:In linear algebra, a hyperplane is a subspace of one dimension less than the ambient space, which is not the geometric object of a hypercuboid.