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PlanarFaceList
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PlanarFaceList

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

The list of faces of a planar graph:

In[2]:=2
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https://wolfram.com/xid/0k71lnulmvbne-fx0ku8
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0k71lnulmvbne-kpunpp
Out[3]=3

The three-dimensional HypercubeGraph is planar:

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-uqu835
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0k71lnulmvbne-jvehcb
Out[2]=2

Scope  (4)Survey of the scope of standard use cases

PlanarFaceList works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-vgpqv0
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-gx301e
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-qfieye
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-e9iyk9
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

Color the graph of a trabecular bone structure:

In[7]:=7
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https://wolfram.com/xid/0k71lnulmvbne-z8er5t
In[10]:=10
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https://wolfram.com/xid/0k71lnulmvbne-gfyvsh
In[11]:=11
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https://wolfram.com/xid/0k71lnulmvbne-ikvgsn
Out[11]=11

Find faces and corresponding colors:

In[13]:=13
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https://wolfram.com/xid/0k71lnulmvbne-nz0khp
In[19]:=19
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https://wolfram.com/xid/0k71lnulmvbne-i30vqj

Color faces:

In[15]:=15
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https://wolfram.com/xid/0k71lnulmvbne-hdmpon
In[20]:=20
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https://wolfram.com/xid/0k71lnulmvbne-bg69bg
Out[20]=20

Properties & Relations  (2)Properties of the function, and connections to other functions

Use DualPlanarGraph to get the dual of planar graphs:

In[8]:=8
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https://wolfram.com/xid/0k71lnulmvbne-f1utis
Out[8]=8

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

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-7bzjh7
Out[1]=1

Possible Issues  (3)Common pitfalls and unexpected behavior

PlanarFaceList returns faces based on the given layout:

In[3]:=3
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https://wolfram.com/xid/0k71lnulmvbne-urzwl8
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0k71lnulmvbne-f3nede
Out[4]=4

PlanarFaceList returns faces based on the given coordinates:

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-dpmqs0
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0k71lnulmvbne-ky3zpl
Out[2]=2

PlanarFaceList can return non-simple faces:

In[1]:=1
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https://wolfram.com/xid/0k71lnulmvbne-gdjzja
Out[1]=1
Wolfram Research (2021), PlanarFaceList, Wolfram Language function, https://reference.wolfram.com/language/ref/PlanarFaceList.html.
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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.

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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.

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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

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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 ]}

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@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 ]}

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@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 ]}