# PlanarFaceList

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.
• 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 all

## 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_2024_planarfacelist, author="Wolfram Research", title="{PlanarFaceList}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/PlanarFaceList.html}", note=[Accessed: 15-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_planarfacelist, organization={Wolfram Research}, title={PlanarFaceList}, year={2021}, url={https://reference.wolfram.com/language/ref/PlanarFaceList.html}, note=[Accessed: 15-June-2024 ]}