Relating to polyhedra or solid shapes.

Characterized by multiple flat surfaces or facets.

Pertaining to geometric structures with various dimensions.

Involving complex multi-faced figures in mathematics.

Describing objects with diverse planar boundaries.

**Polytopal Geometry**: Study of polytopes and their properties.

**Convex Polytope**: A bounded convex polyhedron in higher dimensions.

**Regular Polytope**: Symmetrical, uniform shapes generalized from polygons.

**Star Polytope**: Non-convex polytopes with star-like structure.

**Simplicial Complexes**: Combinations of simplices forming a topological space.

**Polyhedral Complexes**: Union of various dimensional polytopes sharing faces.