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:

Introduced in 2019
 (12.0)