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PolyhedralSets

  

Faces

  

get the faces of a polyhedral set

  

ID

  

get the identifier of a polyhedral set

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Faces(polyset)

Faces(polyset, dimension = d)

Faces(polyset, faceid = id)

ID(polyset)

Parameters

polyset

-

polyhedral set

dimension

-

(optional) integer greater than or equal to , dimension of faces to be returned, defaults to one less than the dimension of polyset to return its facets

faceid

-

(optional) integer or a set or list of integers indexing faces of polyset

Description

• 

The calling sequences Faces(polyset) and Faces(polyset, dimension = d) return a list of polyhedral sets that are -faces of polyset.  Faces(polyset) uses a default value of dimension = Dimension(polyset) - 1, returning the facets of polyset.  If there are no faces of dimension d (e.g. asking for vertices of a half-space), an empty list is returned.

• 

The PolyhedralSets[Vertices] (or, PolyhedralSets[Vertexes]) command is shorthand for Faces(polyset, dimension = 0).  Similarly, PolyhedralSets[Edges] is shorthand for Faces(polyset, dimension = 1), and PolyhedralSets[Facets] is shorthand for Faces(polyset).

• 

A particular face can be retrieved via Faces(polyset, faceid = id).  The identification number id corresponds to those displayed on the graph returned by PolyhedralSets[Graph].

• 

The ID number of a given set can alternatively by obtained with the ID command.  This returns an integer that identifies a set relative to its faces.  Two unrelated polyhedral sets can have the same ID number, but the faces of a given polyhedral set will always have unique ID numbers.

Examples

Get the facets of a tetrahedron

(1)

Plot the faces individually (which will give them each a different color).

The edges of the 5 dimensional simplex are:

(2)

(3)

ID numbers are used to identify the faces of a given set, but different unrelated sets may have the same ID number.

(4)

The faces of a set form a universe, within which the ID numbers uniquely identify members of the graph of the set.

(5)

(6)

Compatibility

• 

The PolyhedralSets[Faces] and PolyhedralSets[ID] commands were introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

PolyhedralSets[VerticesAndRays]

PolyhedralSets[Dimension]

PolyhedralSets[Graph]

GraphTheory

GraphTheory[DrawGraph]

PolyhedralSets[PolyhedralSet]

PolyhedralSets

 


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