Polyhedron

Polyhedron[{f1,,fn}]

represents a filled polyhedron inside the closed surfaces with polygon faces fi.

Polyhedron[{f1,,fn}{{g1,,gm},}]

represents a polyhedron with voids {g1,,gm},.

Polyhedron[{poly1,poly2,}]

represents a collection of polyhedra polyi.

Polyhedron[{p1,,pn},data]

represents a polyhedron in which coordinates given as integers i in data are taken to be pi.

Details and Options

  • Polyhedron can be used a geometric region and a graphics primitive.
  • Polyhedron[{f1,,fn}] is a volume region, representing all the points inside the closed surface with polygon faces fi.
  • A point is an element of the polyhedron if a ray from the point in any direction crosses the boundary polygon faces an odd number of times.
  • Polyhedron[{f1,,fn}{{g1,,gm},}] specifies a polyhedron with voids consisting of an outer polyhedron Polyhedron[{f1,,fn}] and one or several inner polyhedra Polyhedron[{g1,,gm}],.
  • A point p is an element of the polyhedron if it is in the outer polyhedron but not in any inner polyhedron.
  • Polyhedron[{poly1,poly2,}] is a collection of polyhedra polyi with or without voids and is treated as a union of polyi for geometric computations.
  • Polyhedron[{p1,,pn},data] effectively replaces integers i that appear as coordinates in data by the corresponding pi.
  • Polyhedron[{p1,,pn},{f1,,fn}]polyhedron boundary faces fi with points {po1,,pok}
    Polyhedron[{p1,,pn},{{f1,,fk}{{g1,,gl},}]outer polyhedron boundary faces fi with points {po1,,pok} and inner polyhedron boundary faces gj with points {pv1,,pvl} etc.
    Polyhedron[{p1,,pn},{{b1,,bn},{f1,,fk}{{g1,,gl},},}]a collection of several polyhedra
  • As a geometric region, the polygon faces fi can have any embedding dimension, but must all be simple polygons and have the same embedding dimension.
  • In a graphics, the points of the polygon faces fi can be Scaled and Dynamic expressions.
  • Graphics renderings is affected by directives such as FaceForm, EdgeForm, Texture, Specularity, Opacity and color.
  • The following options and settings can be used in graphics:
  • VertexColorsAutomaticvertex colors to be interpolated
    VertexNormalsAutomaticeffective vertex normals for shading
    VertexTextureCoordinatesNonecoordinates for textures

Examples

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Basic Examples  (1)

A polyhedron:

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Its graphic image:

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Its volume:

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Scope  (11)

Possible Issues  (1)

Introduced in 2019
(12.0)