ConvexPolyhedronQ

ConvexPolyhedronQ[poly]

gives True if the polyhedron poly is convex, and False otherwise.

Details

  • A polyhedron is convex if no line segment between two points ever goes outside the polyhedron.

Examples

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Basic Examples  (2)

Test whether a polyhedron is convex:

ConvexPolyhedronQ gives False for non-convex polyhedrons:

Scope  (3)

ConvexPolyhedronQ works on polyhedrons:

Cube:

Dodecahedron:

Tetrahedron:

Polyhedron with holes:

Polyhedron with disconnected components:

Properties & Relations  (3)

A convex polyhedron is simple:

The OuterPolyhedron of a convex polyhedron is convex:

Convex polyhedrons do not have holes:

The UniformPolyhedron is convex:

Possible Issues  (1)

For nonconstant polyhedron, ConvexPolyhedronQ returns False:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_convexpolyhedronq, author="Wolfram Research", title="{ConvexPolyhedronQ}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/ConvexPolyhedronQ.html}", note=[Accessed: 25-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_convexpolyhedronq, organization={Wolfram Research}, title={ConvexPolyhedronQ}, year={2019}, url={https://reference.wolfram.com/language/ref/ConvexPolyhedronQ.html}, note=[Accessed: 25-September-2021 ]}

CMS

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

APA

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