PolyhedralSets[ExampleSets]
ThreeDimensions
examples of three-dimensional polyhedral sets
Calling Sequence
Parameters
Description
Compatibility
Examples
SetName()
SetName(coords)
SetName(varname)
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
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.
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.
withPolyhedralSets:
withExampleSets
Cube,Cuboctahedron,EmptySet,Hypercube,Hyperoctant,Octahedron,RandomSet,RandomSolid,Simplex,Tetrahedron,TruncatedOctahedron,TruncatedTetrahedron,UniversalSet
Sets created without parameters use the default coordinate names.
t≔Tetrahedron;Plott
t≔{Coordinates:x1,x2,x3Relations:−x1−x2−x3≤1,−x1+x2+x3≤1,x1−x2+x3≤1,x1+x2−x3≤1
Alternatively, the coordinates may be specified using a list of names
c≔Cubex,y,z;Plotc
c≔{Coordinates:x,y,zRelations:−z≤1,z≤1,−y≤1,y≤1,−x≤1,x≤1
Or the root variable name for a set of indexed coordinates can be provided.
o≔Octahedrony;Ploto
o≔{Coordinates:y1,y2,y3Relations:−y1−y2−y3≤1,−y1−y2+y3≤1,−y1+y2−y3≤1,−y1+y2+y3≤1,y1−y2−y3≤1,y1−y2+y3≤1,y1+y2−y3≤1,y1+y2+y3≤1
The facets of a truncated octahedron are triangles and regular hexagons.
tt≔TruncatedTetrahedrony;Plottt
tt≔{Coordinates:y1,y2,y3Relations:−y1−y2−y3≤1,−y1−y2+y3≤53,−y1+y2−y3≤53,−y1+y2+y3≤1,y1−y2−y3≤53,y1−y2+y3≤1,y1+y2−y3≤1,y1+y2+y3≤53
The facets of a truncated octahedron are squares and regular hexagons.
tro≔TruncatedOctahedron;Plottro
tro≔{Coordinates:x1,x2,x3Relations:−x3≤1,x3≤1,−x2≤1,x2≤1,−x1−x2−x3≤32,−x2+x3−x1≤32,−x1≤1,−x3+x2−x1≤32,−x1+x2+x3≤32,x1−x3−x2≤32, and 4 more constraints
The facets of a cuboctahedron are regular triangles and squares.
co≔Cuboctahedron;Plotco
co≔{Coordinates:x1,x2,x3Relations:−x3≤1,x3≤1,−x2≤1,x2≤1,−x1−x2−x3≤2,−x2+x3−x1≤2,−x1≤1,−x3+x2−x1≤2,−x1+x2+x3≤2,x1−x3−x2≤2, and 4 more constraints
See Also
Example n-Dimensional Polyhedral Sets
PolyhedralSets[Display]
PolyhedralSets[PrintLevel]
PolyhedralSets[PolyhedralSet]
PolyhedralSets
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