The mathematical know-how in `polymake` is bundled in so called applications. Applications are software components that can be installed and used independently of each other; however, they are allowed to contain functions that "cross the boundaries".

The list below is aimed to give you just the first idea about the standard applications shipped with `polymake`. Choose an application you are interested in via the menu box in the navigation pane; in the tutorial you will find a lot of examples of what can be done with an application, and the following topics lead you to the reference part describing all user-visible components.

Finally, there are collections of external links to other useful information sources on the corresponding research field.

### polytope

This is the historically first application, and the largest one.

It deals with convex pointed polyhedra. It allows to define a polyhedron either as a convex hull of a point set, an intersection of halfspaces, or as an incidence matrix without any embedding. Then you can ask for a plenty of its (especially combinatorial) properties, construct new polyhedra by modifying it, or study the behavior of the objective functions.

There is a wide range of visualization methods for polyhedra, even for dimensions > 4 and purely combinatorial descriptions, including interfaces to interactive geometry viewers (such as JavaView or geomview), generating PostScript drawings and povray scene files.

### topaz

topology application zoo deals with abstract simplicial complexes. A complex is given as a list of facets. You can ask for its global properties (manifold recognition, homology groups, etc.), explore the local vertex environment (stars, links, etc.), and make a lot of constructions.

The visualization means are constrained, as they are mostly based on the graph (1-skeleton) of a complex.

### surface

This is the beginning of an application treating polyhedral surfaces, that is, closed polyhedral 2-manifolds. For the start, the application provides some basic combinatorial properties and visualization.