A major innovation in Mathematica is full integration of geometric computing. Based on an exceptionally powerful geometry engine created at Wolfram Research, Mathematica builds on its unique strengths in numeric and algebraic computing, as well as graphics, to make geometric computing an immediately accessible tool for general computation.

• Adaptive plotting of arbitrary equality- and inequality-defined regions in 2D and 3D.
• Integration, minimization, and plotting over arbitrary implicitly defined regions.
• Geometric search in arbitrary dimensions with arbitrary metrics, including strings, with optimized repeated query mechanism.
• Support for symbolic geometric transformations in any number of dimensions.
• Complete built-in database of named polyhedra, with all geometric and other properties.
• Support for import and export of standard geometry formats (DXF, PLY, BYU, X3D, ...)

Find Regions Defined by Inequalities	Regions Are Found Adaptively	3D Implicit Regions
Plot over Arbitrary Regions	Geometric Searching for Nearest Neighbors	Compute Geometric Transforms Symbolically
The World's Largest Collection of Data on Polyhedra	Use Arbitrary Implicit Regions to Visualize Surfaces