22572: first draft of polyhedra tutorial

src/doc/en/thematic_tutorials/geometry.rst

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+.. -*- coding: utf-8 -*-
+.. _geometry:
+
+=============================================
+Tutorials for the Geometry module of Sage
+=============================================
+
+.. MODULEAUTHOR:: sarah-marie belcastro <smbelcas@toroidalsnark.net>, Jean-Philippe Labbé <labbe@math.fu-berlin.de>
+
+These notes explain how to use Sage for computations related to geometry in Sage. 
+So far, the tutorials cover mostly things related to polyhedral computations.
+
+
+.. toctree::
+   :maxdepth: 2
+
+   geometry/polytutorial
+   geometry/lectures
+   geometry/new_from_old
+   geometry/related_objects
+   geometry/is_this_polyhedron
+   geometry/tips
+   geometry/visualization
+   geometry/polytope_tikz

src/doc/en/thematic_tutorials/geometry/is_this_polyhedron.rst

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+.. -*- coding: utf-8 -*-
+
+.. linkall
+
+.. _is_this_polyhedron:
+
+==============================================================
+Is this polyhedron ...
+==============================================================
+
+.. MODULEAUTHOR:: Jean-Philippe Labbé <labbe@math.fu-berlin.de>
+
+Once a polyhedron object is constructed, it is often useful to check if it has certain 
+properties.
+
+Here is a list of properties that Sage can check.
+
+.. note::
+
+    The following list may note be complete due to recent additions of features. You can 
+    check by making a :code:`tab` completion after typing :code:`is_` to see which methods
+    are available.
+
+... combinatorially isomorphic to this one?
+==============================================================
+
+Two polyhedra are *combinatorially isomorphic* if their face lattices are isomorphic.
+
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_combinatorially_isomorphic`
+
+... compact/a polytope?
+==============================================================
+
+A compact polyhedron is also called a *polytope*.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_compact`
+
+... empty?
+==============================================================
+
+This function although sounding trivial is very important!
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_empty`
+
+... full-dimensional?
+==============================================================
+
+A polyhedron is full dimensional when it does not have any equations in its
+:math:`H`-representation.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_full_dimensional`
+
+... a lattice polytope?
+==============================================================
+
+This functions checks for compactness and if the base ring is :math:`\mathbb{Z}`.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_lattice_polytope`
+
+... inscribed on a sphere?
+==============================================================
+
+This functions checks if the vertices of the polyhedron lie on a sphere.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_inscribed`
+
+... a Minkowski sum of this other one?
+==============================================================
+
+This functions checks if the polyhedron can be used to produce another using a
+Minkowski sum.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_Minkowski_summand`
+
+... neighborly?
+==============================================================
+
+This functions checks if the polyhedron had full skeleton until hafl of the
+dimension.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_neighborly`
+
+... reflexive?
+==============================================================
+
+This functions checks if the polar of a lattice polytope is also a lattice
+polytope.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base_ZZ.Polyhedron_ZZ.is_reflexive`
+
+... simple? (Aren't they all?)
+==============================================================
+
+This functions checks if the degree of all vertices is equal to the dimension
+of the polytope.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_simple`
+
+... simplicial?
+==============================================================
+
+Simplicial polytopes have only simplices as faces.
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_simplicial`
+
+... the simplex?
+==============================================================
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_simplex`
+
+... the whole space?
+==============================================================
+
+Reference manual: :meth:`sage.geometry.polyhedron.base.Polyhedron_base.is_universe`