Polyhedra

(need java)

Equivariant polyhedral surfaces

A convex parabolic polyhedron: the convex hull (in a projective model) of the orbit of one point in the hyperbolic space for the action of a group of isometries acting cocompactly on a horosphere click here
(only a finite number of vertices on the picture)

The same as above, with more vertices (longer to display) click here

A convex Fuchsian polyhedron: the convex hull of the orbit of one point in the Minkowski space for the action of a group of isometries acting cocompactly on the hyperbolic plane click here (only a finite number of vertices on the picture). Here is the convex hull of one point and its iterate by the generators of the group.

The same as above, with a different point click here

A dual picture (orbit of planes) click here

The same as above, same group action but different plane click here

This should have been a convex Fushian polyhedron in a projective model of hyperbolic space…