SnapPea

SnapPea: Mathematics Software for Hyperbolic 3-Manifolds

A software alternative for working with hyperbolic 3-manifolds, SnapPea enables users to create and visualize 3D models of geometric shapes and analyze their properties.

What is SnapPea?

SnapPea is a specialized mathematics software application used for studying and analyzing hyperbolic 3-manifolds. A 3-manifold is a type of topological space in mathematics that resembles our physical 3D space locally, but may have different global properties. Hyperbolic 3-manifolds have a constant negative curvature, similar to a saddle shape.

SnapPea was created by Jeff Weeks as an interactive tool for mathematicians and physicists to visualize and compute properties of hyperbolic 3-manifolds. Its key features include:

• An intuitive graphical interface for building and manipulating 3D models of hyperbolic shapes and spaces.
• Algorithms for computing invariants and properties like volume, cusp structure, and symmetry groups.
• Automatic trivialization and decomposition tools for analyzing manifolds.
• Census databases of thousands of known hyperbolic 3-manifolds.
• Integration with Weeks' software for computing hyperbolic structures from gluing data.

While targeted at research mathematicians, SnapPea also includes educational information and tutorials for students learning about hyperbolic geometry and 3-manifolds. Its visualization capabilities provide valuable geometric intuition to complement analytical understanding.

SnapPea continues to be developed and maintained by Jeff Weeks. While proprietary, free licenses are available for academic research use. Compatible with Windows, Mac, and Linux systems.

SnapPea Features

Official Links