PlanarFaceList

PlanarFaceList[g]

gives the list of faces of the planar graph g.

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

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Basic Examples  (2)

The list of faces of a planar graph:

The three-dimensional HypercubeGraph is planar:

Scope  (4)

PlanarFaceList works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Applications  (1)

Color the graph of a trabecular bone structure:

Find faces and corresponding colors:

Color faces:

Properties & Relations  (2)

Use DualPlanarGraph to get the dual of planar graphs:

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

Possible Issues  (3)

PlanarFaceList returns faces based on the given layout:

PlanarFaceList returns faces based on the given coordinates:

PlanarFaceList can return non-simple faces:

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.

CMS

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

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: 30-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: 30-July-2025 ]}