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OldPolyhedra :: polyhedra

polyhedra -- computes all polyhedra of a polyhedral complex of a certain dimension

Synopsis

Description

polyhedra computes the List of all Polyhedra in PC of dimension d.

i1 : PC = polyhedralComplex hypercube 3

o1 = {ambient dimension => 3             }
      number of generating polyhedra => 1
      top dimension of the polyhedra => 3

o1 : PolyhedralComplex
i2 : L = polyhedra(2,PC)

o2 = {{ambient dimension => 3           }, {ambient dimension => 3         
       dimension of lineality space => 0    dimension of lineality space =>
       dimension of polyhedron => 2         dimension of polyhedron => 2   
       number of facets => 4                number of facets => 4          
       number of rays => 0                  number of rays => 0            
       number of vertices => 4              number of vertices => 4        
     ------------------------------------------------------------------------
      }, {ambient dimension => 3           }, {ambient dimension => 3      
     0    dimension of lineality space => 0    dimension of lineality space
          dimension of polyhedron => 2         dimension of polyhedron => 2
          number of facets => 4                number of facets => 4       
          number of rays => 0                  number of rays => 0         
          number of vertices => 4              number of vertices => 4     
     ------------------------------------------------------------------------
         }, {ambient dimension => 3           },
     => 0    dimension of lineality space => 0  
             dimension of polyhedron => 2       
             number of facets => 4              
             number of rays => 0                
             number of vertices => 4            
     ------------------------------------------------------------------------
     {ambient dimension => 3           }}
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o2 : List

To actually see the polyhedra of the complex we can look at their vertices, for example:

i3 : apply(L,vertices)

o3 = {| -1 -1 -1 -1 |, | 1  1  1  1 |, | -1 1  -1 1  |, | -1 1  -1 1 |, | -1
      | -1 1  -1 1  |  | -1 1  -1 1 |  | -1 -1 -1 -1 |  | 1  1  1  1 |  | -1
      | -1 -1 1  1  |  | -1 -1 1  1 |  | -1 -1 1  1  |  | -1 -1 1  1 |  | -1
     ------------------------------------------------------------------------
     1  -1 1  |, | -1 1  -1 1 |}
     -1 1  1  |  | -1 -1 1  1 |
     -1 -1 -1 |  | 1  1  1  1 |

o3 : List

Ways to use polyhedra :

For the programmer

The object polyhedra is a method function.