PlanarFaceList
✖
PlanarFaceList
Details

- PlanarFaceList is also known as faces or regions.
- PlanarFaceList is typically used to give vertices of the dual of a planar graph.
- PlanarFaceList[g] gives a list of faces {f1,f2,…} of the graph g, where the face fi={vi1,vi2,…} is bounded by vertices vij and edges between them.

Examples
open allclose allBasic Examples (2)Summary of the most common use cases
The list of faces of a planar graph:

https://wolfram.com/xid/0k71lnulmvbne-fx0ku8


https://wolfram.com/xid/0k71lnulmvbne-kpunpp

The three-dimensional HypercubeGraph is planar:

https://wolfram.com/xid/0k71lnulmvbne-uqu835


https://wolfram.com/xid/0k71lnulmvbne-jvehcb

Scope (4)Survey of the scope of standard use cases
PlanarFaceList works with undirected graphs:

https://wolfram.com/xid/0k71lnulmvbne-vgpqv0


https://wolfram.com/xid/0k71lnulmvbne-gx301e


https://wolfram.com/xid/0k71lnulmvbne-qfieye


https://wolfram.com/xid/0k71lnulmvbne-e9iyk9

Applications (1)Sample problems that can be solved with this function
Color the graph of a trabecular bone structure:

https://wolfram.com/xid/0k71lnulmvbne-z8er5t

https://wolfram.com/xid/0k71lnulmvbne-gfyvsh

https://wolfram.com/xid/0k71lnulmvbne-ikvgsn

Find faces and corresponding colors:

https://wolfram.com/xid/0k71lnulmvbne-nz0khp

https://wolfram.com/xid/0k71lnulmvbne-i30vqj

https://wolfram.com/xid/0k71lnulmvbne-hdmpon

https://wolfram.com/xid/0k71lnulmvbne-bg69bg

Properties & Relations (2)Properties of the function, and connections to other functions
Use DualPlanarGraph to get the dual of planar graphs:

https://wolfram.com/xid/0k71lnulmvbne-f1utis

Use FindPlanarColoring to find a coloring for the faces of planar graphs:

https://wolfram.com/xid/0k71lnulmvbne-7bzjh7

Possible Issues (3)Common pitfalls and unexpected behavior
PlanarFaceList returns faces based on the given layout:

https://wolfram.com/xid/0k71lnulmvbne-urzwl8


https://wolfram.com/xid/0k71lnulmvbne-f3nede

PlanarFaceList returns faces based on the given coordinates:

https://wolfram.com/xid/0k71lnulmvbne-dpmqs0


https://wolfram.com/xid/0k71lnulmvbne-ky3zpl

PlanarFaceList can return non-simple faces:

https://wolfram.com/xid/0k71lnulmvbne-gdjzja

Wolfram Research (2021), PlanarFaceList, Wolfram Language function, https://reference.wolfram.com/language/ref/PlanarFaceList.html.
Text
Wolfram Research (2021), PlanarFaceList, Wolfram Language function, https://reference.wolfram.com/language/ref/PlanarFaceList.html.
Wolfram Research (2021), PlanarFaceList, Wolfram Language function, https://reference.wolfram.com/language/ref/PlanarFaceList.html.
CMS
Wolfram Language. 2021. "PlanarFaceList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PlanarFaceList.html.
Wolfram Language. 2021. "PlanarFaceList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PlanarFaceList.html.
APA
Wolfram Language. (2021). PlanarFaceList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PlanarFaceList.html
Wolfram Language. (2021). PlanarFaceList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PlanarFaceList.html
BibTeX
@misc{reference.wolfram_2025_planarfacelist, author="Wolfram Research", title="{PlanarFaceList}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/PlanarFaceList.html}", note=[Accessed: 10-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_planarfacelist, organization={Wolfram Research}, title={PlanarFaceList}, year={2021}, url={https://reference.wolfram.com/language/ref/PlanarFaceList.html}, note=[Accessed: 10-July-2025
]}