Basiskörper

Basiskörper (German for "base body") is a term used in geometry to denote a foundational geometric solid that serves as a reference or starting point in a construction, transformation, or comparison. The exact definition varies with context and author, but the central idea is that the Basiskörper is the canonical object from which others are derived by operations such as scaling, rotation, translation, or Minkowski addition.

In convex geometry and the theory of normed spaces, the Basiskörper often coincides with the unit ball of a norm. This Basiskörper encodes the metric structure of the space: its shape determines lengths, angles, and dual relationships. The dual or polar body with respect to a given origin is a closely related concept, giving rise to the corresponding dual norm.

Beyond pure analysis, the Basiskörper appears in tiling and crystallography as a fundamental domain or primitive cell that, under symmetry operations, generates the full figure or lattice. In computer graphics, a Basiskörper is a basic primitive shape (such as a cube or sphere) used as the building block for more complex models through transformations and composition.

Because German mathematical terminology is not universally standardized, Basiskörper is not a fixed technical term; it is a descriptive label whose precise meaning depends on the text. Related ideas include convex body, unit ball, norm, Minkowski sum, and dual body.