PolyhedronGenus

PolyhedronGenus[poly]

gives the genus of the polyhedron poly.

Details

  • PolyhedronGenus is also known as genus.
  • PolyhedronGenus gives the maximum number of cuttings along non-intersecting closed simple curves on the surface of the polyhedron without disconnecting the polyhedron.

Examples

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Basic Examples  (1)

Genus of a polyhedron:

Scope  (3)

PolyhedronGenus works on polyhedrons:

Tetrahedron:

Hexahedron:

Polyhedron with holes:

Polyhedrons with disconnected components:

Properties & Relations  (3)

Use EulerCharacteristic to compute PolyhedronGenus for a simple polyhedron:

Convex polyhedron has zero genus:

The genus of UniformPolyhedron is 0:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_polyhedrongenus, author="Wolfram Research", title="{PolyhedronGenus}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolyhedronGenus.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_polyhedrongenus, organization={Wolfram Research}, title={PolyhedronGenus}, year={2019}, url={https://reference.wolfram.com/language/ref/PolyhedronGenus.html}, note=[Accessed: 21-February-2025 ]}