Sage includes classes for hyperplane arrangements, polyhedra, toric varieties (including polyhedral cones and fans), triangulations and some other helper classes and functions.
sage/geometry/hyperplane_arrangement/arrangement sage/geometry/hyperplane_arrangement/library sage/geometry/hyperplane_arrangement/hyperplane sage/geometry/hyperplane_arrangement/affine_subspace sage/geometry/hyperplane_arrangement/plot
sage/geometry/polyhedron/library sage/geometry/polyhedron/constructor sage/geometry/polyhedron/parent sage/geometry/polyhedron/representation sage/geometry/polyhedron/plot sage/geometry/polyhedron/face sage/geometry/polyhedron/cdd_file_format sage/geometry/polyhedron/modules/formal_polyhedra_module
sage/geometry/lattice_polytope sage/geometry/polyhedron/lattice_euclidean_group_element sage/geometry/polyhedron/palp_database sage/geometry/polyhedron/ppl_lattice_polygon sage/geometry/polyhedron/ppl_lattice_polytope
sage/geometry/toric_lattice sage/geometry/cone sage/geometry/cone_catalog sage/geometry/fan sage/geometry/fan_morphism sage/geometry/point_collection sage/geometry/toric_plotter sage/rings/polynomial/groebner_fan
sage/geometry/polyhedron/base sage/geometry/polyhedron/base_QQ sage/geometry/polyhedron/base_ZZ sage/geometry/polyhedron/base_RDF
sage/geometry/polyhedron/backend_cdd sage/geometry/polyhedron/backend_field sage/geometry/polyhedron/backend_normaliz sage/geometry/polyhedron/backend_polymake sage/geometry/polyhedron/backend_ppl sage/geometry/polyhedron/double_description sage/geometry/polyhedron/double_description_inhomogeneous
sage/geometry/triangulation/point_configuration sage/geometry/triangulation/base sage/geometry/triangulation/element
sage/geometry/convex_set sage/geometry/linear_expression sage/geometry/newton_polygon sage/geometry/relative_interior sage/geometry/ribbon_graph sage/geometry/pseudolines sage/geometry/voronoi_diagram
sage/geometry/fan_isomorphism sage/geometry/hasse_diagram sage/geometry/integral_points sage/geometry/hyperplane_arrangement/check_freeness