SimplePolyhedronQ

SimplePolyhedronQ[poly]

gives True if the polyhedron poly is simple and False otherwise.

Details

  • A polyhedron is simple if it has no voids and non-intersecting boundary faces.
  • A simple polyhedron is topologically equivalent to a ball.

Examples

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Basic Examples  (2)

Test whether a polyhedron is simple:

SimplePolyhedronQ gives False for non-simple polyhedrons:

Scope  (3)

SimplePolyhedronQ works on polyhedrons:

Cube:

Dodecahedron:

Tetrahedron:

Polyhedron with holes:

Polyhedrons with disconnected components:

Properties & Relations  (3)

A convex polyhedron is simple:

The OuterPolyhedron of a simple polyhedron is simple:

Simple polyhedrons do not have holes:

The UniformPolyhedron is simple:

Possible Issues  (1)

For nonconstant polyhedrons, SimplePolyhedronQ returns False:

Wolfram Research (2019), SimplePolyhedronQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SimplePolyhedronQ.html.

Text

Wolfram Research (2019), SimplePolyhedronQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SimplePolyhedronQ.html.

BibTeX

@misc{reference.wolfram_2020_simplepolyhedronq, author="Wolfram Research", title="{SimplePolyhedronQ}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/SimplePolyhedronQ.html}", note=[Accessed: 02-March-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_simplepolyhedronq, organization={Wolfram Research}, title={SimplePolyhedronQ}, year={2019}, url={https://reference.wolfram.com/language/ref/SimplePolyhedronQ.html}, note=[Accessed: 02-March-2021 ]}

CMS

Wolfram Language. 2019. "SimplePolyhedronQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SimplePolyhedronQ.html.

APA

Wolfram Language. (2019). SimplePolyhedronQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SimplePolyhedronQ.html