====== BigObject PlanarNet<Scalar> ======
//from application [[..:fan|fan]]//\\
\\
 A special big object class devoted to planar unfoldings of 3-polytopes.  Its main functionality is the visualization.

  ? Type Parameters:
  :: ''Scalar'': inherited from ''Scalar''
  ? derived from:
  : ''[[..:fan:PolyhedralComplex |PolyhedralComplex]]''
  ? Example:
  :: To visualize a planar net of some Johnson solid (with flaps, such that you can print, cut and glue):
  :: <code perl> > planar_net(polytope::johnson_solid(52))->VISUAL->FLAPS;
</code>
===== Properties =====

==== Combinatorics ====
 These properties capture combinatorial information of the object.  Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.
----
{{anchor:dual_tree:}}
  ?  **''DUAL_TREE''**
  :: The spanning tree in the ''[[..:polytope:Polytope#DUAL_GRAPH |DUAL_GRAPH]]'' which defines the layout. Endoded as a list of edges, directed away from the root facet. Indices correspond to ''[[..:fan:PolyhedralComplex#MAXIMAL_POLYTOPES |MAXIMAL_POLYTOPES]]'' as well as ''[[..:polytope:Cone#FACETS |FACETS]]''.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Pair |Pair]]<[[..:common#Int |Int]],[[..:common#Int |Int]]%%>>%%''


----
{{anchor:flaps:}}
  ?  **''FLAPS''**
  :: List of directed edges in the primal graph ''[[..:polytope:Polytope#GRAPH |GRAPH]]'' which need flaps for gluing. Indices correspond to ''[[..:fan:PolyhedralComplex#VERTICES |VERTICES]]''.  The orientation is chosen such that the facet in the layout is always on the left. In fact, the flaps define a spanning tree of ''[[..:polytope:Polytope#GRAPH |GRAPH]]''.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Pair |Pair]]<[[..:common#Int |Int]],[[..:common#Int |Int]]%%>>%%''


----
{{anchor:vf_map:}}
  ?  **''VF_MAP''**
  :: Map which tells which vertex/facet pair of the 3-polytope is mapped to which vertex of the planar net. The dependence on the facets comes from the fact that most ''[[..:polytope:Polytope#VERTICES |VERTICES]]'' occur more than once in the planar net. The inverse is ''[[..:fan:PlanarNet#VF_MAP_INV |VF_MAP_INV]]''.
    ? Type:
    :''[[..:common#Map |Map]]<[[..:common#Pair |Pair]]<[[..:common#Int |Int]],[[..:common#Int |Int]]>,[[..:common#Int |Int]]>''


----
{{anchor:vf_map_inv:}}
  ?  **''VF_MAP_INV''**
  :: Map which tells how the ''[[..:fan:PolyhedralComplex#VERTICES |VERTICES]]'' of the planar net are mapped to the ''[[..:polytope:Polytope#VERTICES |VERTICES]]'' of the 3-polytope. Inverse of ''[[..:fan:PlanarNet#VF_MAP |VF_MAP]]''.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Int |Int]]>''


----
{{anchor:vif_cyclic_normal:}}
  ?  **''VIF_CYCLIC_NORMAL''**
  :: Counter clockwise ordering of the ''[[..:fan:PolyhedralComplex#VERTICES |VERTICES]]'' in each ''[[..:fan:PolyhedralComplex#MAXIMAL_POLYTOPES |MAXIMAL_POLYTOPES]]''. This is a copy of the property ''[[..:polytope:Polytope#VIF_CYCLIC_NORMAL |VIF_CYCLIC_NORMAL]]'' of ''[[..:fan:PlanarNet#POLYTOPE |POLYTOPE]]''.
    ? Type:
    :''[[..:common#Array |Array]]<[[..:common#Array |Array]]<[[..:common#Int |Int]]%%>>%%''


----

==== Geometry ====
 These properties capture geometric information of the object.  Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.
----
{{anchor:polytope:}}
  ?  **''POLYTOPE''**
  :: The corresponding 3-polytope.
    ? Type:
    :''[[..:polytope:Polytope |Polytope]]<Scalar>''


----
===== Methods =====

==== Visualization ====
 These methods are for visualization.
----
{{anchor:visual:}}
  ?  **''VISUAL()''**
  :: This function is the main purpose of the entire class ''[[..:fan:PlanarNet |PlanarNet]]''.
    ? Options:
    : option list ''[[..:common#Visual_Polygons_decorations |Visual::Polygons::decorations]]''
    ? Returns:
    :''[[..:fan:Visual_PlanarNet |Visual::PlanarNet]]''


----