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PolyhedralSets[ExampleSets]

  

ThreeDimensions

  

Example of Three Dimensional Polyhedral Sets

 

Calling Sequence

Parameters

Description

Compatibility

Examples

Calling Sequence

SetName()

SetName(coords)

SetName(varname)

Parameters

SetName

-

procedure name; one of Tetrahedron, Cube, Octahedron, TruncatedTetrahedron, TruncatedOctahedron, or Cuboctahedron

coords

-

list of names; the set's three coordinates

varname

-

name; variable name to use in forming the coordinates

Description

• 

The Tetrahedron, Cube, Octahedron, TruncatedTetrahedron, TruncatedOctahedron, and Cuboctahedron commands create polyhedral sets in three dimensions.  The calling sequence with no arguments, SetName(), uses the default coordinates for the set's ambient space.  Alternatively, the coordinates can be specified via SetName(coords) or generated as indexed variables with variable varname as their root via SetName(varname).

• 

The tetrahedron, cube and octahedron are regular polyhedra.  The truncated tetrahedron, truncated octahedron and cuboctahedron are semiregular polyhedra, whose facets consist of different types of regular polygons.

Compatibility

• 

The Tetrahedron, Cube, Octahedron, TruncatedTetrahedron, TruncatedOctahedron, and Cuboctahedron commands were introduced in Maple 2015.

• 

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

Examples

withPolyhedralSets:

withExampleSets

Cube,Cuboctahedron,EmptySet,Hypercube,Hyperoctant,Octahedron,RandomSet,RandomSolid,Simplex,Tetrahedron,TruncatedOctahedron,TruncatedTetrahedron,UniversalSet

(1)

Sets created without parameters use the default coordinate names

tTetrahedron;Plott

t{Coordinates:x1,x2,x3Relations:x1x2x31,x1+x2+x31,x1x2+x31,x1+x2x31

Alternatively, the coordinates may be specified using a list of names

cCubex,y,z;Plotc

c{Coordinates:x,y,zRelations:z1,z1,y1,y1,x1,x1

Or the root variable name for a set of indexed coordinates can be provided

oOctahedrony;Ploto

o{Coordinates:y1,y2,y3Relations:y1y2y31,y1y2+y31,y1+y2y31,y1+y2+y31,y1y2y31,y1y2+y31,y1+y2y31,y1+y2+y31

The facets of a truncated octahedron are triangles and regular hexagons

ttTruncatedTetrahedrony;Plottt

tt{Coordinates:y1,y2,y3Relations:y1y2y31,y1y2+y353,y1+y2y353,y1+y2+y31,y1y2y353,y1y2+y31,y1+y2y31,y1+y2+y353

The facets of a truncated octahedron are squares and regular hexagons

troTruncatedOctahedron;Plottro

tro{Coordinates:x1,x2,x3Relations:x31,x31,x21,x21,x3x2x132,x2+x3x132,x11,x3+x2x132,x3+x2x132,x1x3x232, and 4 more constraints

The facets of a cuboctahedron are regular triangles and squares

coCuboctahedron;Plotco

co{Coordinates:x1,x2,x3Relations:x31,x31,x21,x21,x3x2x12,x2+x3x12,x11,x3+x2x12,x3+x2x12,x1x3x22, and 4 more constraints

See Also

Example n-Dimensional Polyhedral Sets

PolyhedralSets[Display]

PolyhedralSets[PrintLevel]

PolyhedralSets[PolyhedralSet]

PolyhedralSets

 


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