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--- tutorial:polytope_semantics [2011/11/21 15:47] – [Without coordinates: Combinatorics] there was a ")" too mutch assarf
+++ tutorial:polytope_semantics [2017/03/29 14:04] – [Special Cases] hnagel
@@ Line 30: / Line 30: @@
 ==== Special Cases ====
+Most of what comes below is a consequence of the design decisions explained above.
 === Empty polytopes ===
@@ Line 42: / Line 44: @@
 === Zero-dimensional polytopes ===
-A zero-dimensional polytope is a single point.  In our model it has one vertex and one facet.
+A zero-dimensional polytope is a single point.  In our model it has one vertex and one facet (the far hyperplane).
 ''VERTICES_IN_FACETS'' is a 1-by-1 matrix with a zero entry.  This means that the single vertex does //not// lie on the single facet.
 Such a polytope is both simple and simplicial, i.e. it is a simplex.
+=== Zero-dimensional fans ===
+A zero-dimensional fan can e.g. be defined via <code>$f=new PolyhedralFan(RAYS=>[], MAXIMAL_CONES=>[[]]);</code>
+==== Summing Up ====
+For instance we have four possibilities which can occur for ''VERTICES''. The property
+  * does not exist (it is not listed in ''list_properties''): This basically means that the property is not derived/calculated, yet.
+  * exists and is set to ''undef'': Polymake is not able to derive this property with the given properties. The polytope may be empty or not.
+  * exists and is empty: So the polytope is empty.
+  * exists and is neither set to ''undef'' nor is empty: Our polytope is not empty and the property returns what you expect.