EulerCharacteristic
EulerCharacteristic[poly]
gives the Euler characteristic of a poly.
Details
- EulerCharacteristic is also known as Euler number or Euler–Poincaré characteristic.
- EulerCharacteristic is a topological invariant that describes the shape of the polyhedron, regardless of the way it is bent.
- The Euler characteristic
for a polyhedron is given by 
, where 
is the number of vertices, 
the number of edges and 
the number of faces. - A polyhedron with
voids and 
tunnels satisfies 
. - The Euler characteristic for a mesh region is given by χ=
(-1)nMeshCellCount[poly,n].
Examples
open allclose allScope (4)
EulerCharacteristic works on polyhedrons:
Polyhedrons with disconnected components:
EulerCharacteristic works on mesh regions:
Properties & Relations (3)
Use EulerCharacteristic to compute PolyhedronGenus for a simple polyhedron:
Euler characteristic of a convex polyhedron equals 2:
Euler characteristic of UniformPolyhedron is 2:
Text
Wolfram Research (2019), EulerCharacteristic, Wolfram Language function, https://reference.wolfram.com/language/ref/EulerCharacteristic.html.
CMS
Wolfram Language. 2019. "EulerCharacteristic." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EulerCharacteristic.html.
APA
Wolfram Language. (2019). EulerCharacteristic. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EulerCharacteristic.html