Mathematica's strengths in algebraic computation and graphics as well as numerics combine to bring unprecedented flexibility and power to geometric computation. Making extensive use of original algorithms developed at Wolfram Research, Mathematica's ability to represent and manipulate geometry symbolically allows it for the first time to fully integrate generation, analysis, and rendering of geometrical structures.
Nearest — find nearest points in any number of dimensions with any metric
NearestFunction — a function created to repeatedly find nearest points
Reduce — symbolically reduce real, complex and integer geometry descriptions
LinearProgramming — minimize over finite or infinite polyhedral regions
PolyhedronData — geometrical and structural data on regular polyhedra