BuckyballGraph
✖
BuckyballGraph
Details and Options

- BuckyballGraph is also known as truncated icosahedral graph or fullerene graph.
- BuckyballGraph[] gives the 1-skeleton of the truncated icosahedron.
- BuckyballGraph[n,"I"] gives the 1-skeleton of the
‐Goldberg polyhedron.
- BuckyballGraph[n,"II"] gives the 1-skeleton of the
‐Goldberg polyhedron.
- BuckyballGraph[n] is effectively equivalent to BuckyballGraph[n,"II"].
- BuckyballGraph takes the same options as Graph3D.
-
AlignmentPoint Center the default point in the graphic to align with AnnotationRules {} annotations for graph, edges and vertices AspectRatio Automatic ratio of height to width Axes False whether to draw axes AxesEdge Automatic on which edges to put axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} graphics directives to specify the style for axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic Boxed False whether to draw edges of the bounding box BoxRatios Automatic bounding 3D box ratios BoxStyle {} style specifications for the box ClipPlanes None clipping planes ClipPlanesStyle Automatic style specifications for clipping planes ContentSelectable Automatic whether to allow contents to be selected ControllerLinking False when to link to external rotation controllers ControllerPath Automatic what external controllers to try to use DirectedEdges Automatic whether to interpret Rule as DirectedEdge EdgeLabels Automatic labels and placements for edges EdgeLabelStyle Automatic style to use for edge labels EdgeShapeFunction Automatic generate graphic shapes for edges EdgeStyle Automatic styles for edges EdgeWeight Automatic weights for edges Epilog {} 2D graphics primitives to be rendered after the main plot FaceGrids None grid lines to draw on the bounding box FaceGridsStyle {} style specifications for face grids FormatType TraditionalForm default format type for text GraphHighlight {} graph elements to highlight GraphHighlightStyle Automatic style for highlight GraphLayout Automatic how to lay out vertices and edges ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels, etc. ImageSize Automatic absolute size at which to render the graphic LabelStyle {} style specifications for labels Lighting Automatic simulated light sources to use Method Automatic details of 3D graphics methods to use PerformanceGoal Automatic aspects of performance to try to optimize PlotLabel None a label for the plot PlotRange All range of values to include PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic final display region to be filled PlotTheme Automatic overall style for graph elements PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} 2D graphics primitives to be rendered before the main plot RotationAction "Fit" how to render after interactive rotation SphericalRegion Automatic whether to make the circumscribing sphere fit in the final display area Ticks Automatic specification for ticks TicksStyle {} style specification for ticks TouchscreenAutoZoom False whether to zoom to fullscreen when activated on a touchscreen VertexCoordinates Automatic coordinates for vertices VertexLabels Automatic labels and placements for vertices VertexLabelStyle Automatic style to use for vertex labels VertexShape Automatic graphic shape for vertices VertexShapeFunction Automatic generate graphic shapes for vertices VertexSize Medium size of vertices VertexStyle Automatic styles for vertices VertexWeight Automatic weights for vertices ViewAngle Automatic angle of the field of view ViewCenter Automatic point to display at the center ViewMatrix Automatic explicit transformation matrix ViewPoint {1.3,-2.4,2.} viewing position ViewProjection Automatic projection method for rendering objects distant from the viewer ViewRange All range of viewing distances to include ViewVector Automatic position and direction of a simulated camera ViewVertical {0,0,1} direction to make vertical



List of all options




Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (4)Survey of the scope of standard use cases

https://wolfram.com/xid/0bc6xg52swj6b2i-9b83dr

Generate a class II, order-1 buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-c2453e

Generate a class I, order-3 buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-fa8brm

A class II, order-3 buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-r0gzdq

Generate a directed buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-0ww8tt

Options (77)Common values & functionality for each option
AnnotationRules (3)
Specify an annotation for vertices:

https://wolfram.com/xid/0bc6xg52swj6b2i-tv6rsi


https://wolfram.com/xid/0bc6xg52swj6b2i-hfpnz0


https://wolfram.com/xid/0bc6xg52swj6b2i-wtg2wg


https://wolfram.com/xid/0bc6xg52swj6b2i-7lc57p

DirectedEdges (1)
By default, an undirected graph is generated:

https://wolfram.com/xid/0bc6xg52swj6b2i-iwq8nh

Use DirectedEdges->True to generate a directed graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-hsbm48

EdgeLabels (7)

https://wolfram.com/xid/0bc6xg52swj6b2i-z5279


https://wolfram.com/xid/0bc6xg52swj6b2i-1t3zd

https://wolfram.com/xid/0bc6xg52swj6b2i-hr4015

Use any expression as a label:

https://wolfram.com/xid/0bc6xg52swj6b2i-b7zkda

Use Placed with symbolic locations to control label placement along an edge:

https://wolfram.com/xid/0bc6xg52swj6b2i-fnltmw

Use explicit coordinates to place labels:

https://wolfram.com/xid/0bc6xg52swj6b2i-ndfa94

Vary positions within the label:

https://wolfram.com/xid/0bc6xg52swj6b2i-bg84f5

Place multiple labels using Placed in a wrapper:

https://wolfram.com/xid/0bc6xg52swj6b2i-cj2dt

Any number of labels can be used:

https://wolfram.com/xid/0bc6xg52swj6b2i-dy5run

Place multiple labels using EdgeLabels:

https://wolfram.com/xid/0bc6xg52swj6b2i-33q72

Use automatic labeling by values through Tooltip and StatusArea:

https://wolfram.com/xid/0bc6xg52swj6b2i-dhn5kr

EdgeShapeFunction (6)
Get a list of built-in settings for EdgeShapeFunction:

https://wolfram.com/xid/0bc6xg52swj6b2i-hfmhqu

Undirected edges including the basic line:

https://wolfram.com/xid/0bc6xg52swj6b2i-fjhml

Lines with different glyphs on the edges:

https://wolfram.com/xid/0bc6xg52swj6b2i-lxjrsx

Directed edges including solid arrows:

https://wolfram.com/xid/0bc6xg52swj6b2i-lvr0ss


https://wolfram.com/xid/0bc6xg52swj6b2i-qslbt


https://wolfram.com/xid/0bc6xg52swj6b2i-f6ch7m

Specify an edge function for an individual edge:

https://wolfram.com/xid/0bc6xg52swj6b2i-eczrhp

Combine with a different default edge function:

https://wolfram.com/xid/0bc6xg52swj6b2i-jwjk2c

Draw edges by running a program:

https://wolfram.com/xid/0bc6xg52swj6b2i-j0dznf

https://wolfram.com/xid/0bc6xg52swj6b2i-lsgwlp

EdgeShapeFunction can be combined with EdgeStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-gt52v9

EdgeShapeFunction has higher priority than EdgeStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-cfn5oz

EdgeStyle (4)

https://wolfram.com/xid/0bc6xg52swj6b2i-dx7dg5


https://wolfram.com/xid/0bc6xg52swj6b2i-ffvp7v

EdgeStyle can be combined with EdgeShapeFunction:

https://wolfram.com/xid/0bc6xg52swj6b2i-byw1p6

https://wolfram.com/xid/0bc6xg52swj6b2i-gltig7

EdgeShapeFunction has higher priority than EdgeStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-f7ohq3

https://wolfram.com/xid/0bc6xg52swj6b2i-kw06wx

EdgeStyle can be combined with BaseStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-mwzwu

EdgeStyle has higher priority than BaseStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-ovk4z6

EdgeWeight (3)
Specify a weight for all edges:

https://wolfram.com/xid/0bc6xg52swj6b2i-8fxi6


https://wolfram.com/xid/0bc6xg52swj6b2i-baprxk

Use any numeric expression as a weight:

https://wolfram.com/xid/0bc6xg52swj6b2i-bcptub


https://wolfram.com/xid/0bc6xg52swj6b2i-fibbsw

Specify weights for individual edges:

https://wolfram.com/xid/0bc6xg52swj6b2i-dus88r


https://wolfram.com/xid/0bc6xg52swj6b2i-c3ozib

GraphHighlight (3)
GraphLayout (5)
By default, the layout is chosen automatically:

https://wolfram.com/xid/0bc6xg52swj6b2i-hrq0b5

Specify layouts on special curves:

https://wolfram.com/xid/0bc6xg52swj6b2i-fnopvf

Specify layouts that satisfy optimality criteria:

https://wolfram.com/xid/0bc6xg52swj6b2i-tzfd4

VertexCoordinates overrides GraphLayout coordinates:

https://wolfram.com/xid/0bc6xg52swj6b2i-h4ccju

Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:

https://wolfram.com/xid/0bc6xg52swj6b2i-u259v


https://wolfram.com/xid/0bc6xg52swj6b2i-bd4if

PlotTheme (4)
Base Themes (2)
VertexCoordinates (3)
By default, any vertex coordinates are computed automatically:

https://wolfram.com/xid/0bc6xg52swj6b2i-5spor

Extract the resulting vertex coordinates using AbsoluteOptions:

https://wolfram.com/xid/0bc6xg52swj6b2i-2whoh

Specify a layout function along an ellipse:

https://wolfram.com/xid/0bc6xg52swj6b2i-mwyuvu

https://wolfram.com/xid/0bc6xg52swj6b2i-cvx31k

Use it to generate vertex coordinates for a graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-uukkr

VertexCoordinates has higher priority than GraphLayout:

https://wolfram.com/xid/0bc6xg52swj6b2i-hdij4u

VertexLabels (13)

https://wolfram.com/xid/0bc6xg52swj6b2i-c9ka50


https://wolfram.com/xid/0bc6xg52swj6b2i-i40mcj


https://wolfram.com/xid/0bc6xg52swj6b2i-whkpg

Use any expression as a label:

https://wolfram.com/xid/0bc6xg52swj6b2i-kokbex

Use Placed with symbolic locations to control label placement, including outside positions:

https://wolfram.com/xid/0bc6xg52swj6b2i-csc6y

Symbolic outside corner positions:

https://wolfram.com/xid/0bc6xg52swj6b2i-405x2

https://wolfram.com/xid/0bc6xg52swj6b2i-fjgxt8


https://wolfram.com/xid/0bc6xg52swj6b2i-fg0pin

Symbolic inside corner positions:

https://wolfram.com/xid/0bc6xg52swj6b2i-kfrv7

https://wolfram.com/xid/0bc6xg52swj6b2i-dr87wv

Use explicit coordinates to place the center of labels:

https://wolfram.com/xid/0bc6xg52swj6b2i-cqfi4r

Place all labels at the upper-right corner of the vertex and vary the coordinates within the label:

https://wolfram.com/xid/0bc6xg52swj6b2i-20sv


https://wolfram.com/xid/0bc6xg52swj6b2i-eazh7z

Any number of labels can be used:

https://wolfram.com/xid/0bc6xg52swj6b2i-ftgvi6

Use the argument to Placed to control formatting including Tooltip:

https://wolfram.com/xid/0bc6xg52swj6b2i-cxzeiw

Or StatusArea:

https://wolfram.com/xid/0bc6xg52swj6b2i-nddwmk

Use more elaborate formatting functions:

https://wolfram.com/xid/0bc6xg52swj6b2i-bd9m40

https://wolfram.com/xid/0bc6xg52swj6b2i-cggp96


https://wolfram.com/xid/0bc6xg52swj6b2i-l3s7yb

https://wolfram.com/xid/0bc6xg52swj6b2i-cljxny


https://wolfram.com/xid/0bc6xg52swj6b2i-cqkdbb

https://wolfram.com/xid/0bc6xg52swj6b2i-bjoam1

VertexShapeFunction (11)
Get a list of built-in collections for VertexShapeFunction:

https://wolfram.com/xid/0bc6xg52swj6b2i-cc7w4d

Use built-in settings for VertexShapeFunction in the "Basic" collection:

https://wolfram.com/xid/0bc6xg52swj6b2i-kqz1mq


https://wolfram.com/xid/0bc6xg52swj6b2i-20nhrf


https://wolfram.com/xid/0bc6xg52swj6b2i-wm2s7

Use built-in settings for VertexShapeFunction in the "Rounded" collection:

https://wolfram.com/xid/0bc6xg52swj6b2i-cpul4b


https://wolfram.com/xid/0bc6xg52swj6b2i-cj5ftp

Use built-in settings for VertexShapeFunction in the "Concave" collection:

https://wolfram.com/xid/0bc6xg52swj6b2i-f4ea1p


https://wolfram.com/xid/0bc6xg52swj6b2i-bfhgv4


https://wolfram.com/xid/0bc6xg52swj6b2i-fhb0zi

Combine with a default vertex function:

https://wolfram.com/xid/0bc6xg52swj6b2i-fmawhn

Draw vertices using a predefined graphic:

https://wolfram.com/xid/0bc6xg52swj6b2i-6fiu

Draw vertices by running a program:

https://wolfram.com/xid/0bc6xg52swj6b2i-oroxkx

https://wolfram.com/xid/0bc6xg52swj6b2i-lt54lp

VertexShapeFunction can be combined with VertexStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-djz15m

VertexShapeFunction has higher priority than VertexStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-h9wrh2

https://wolfram.com/xid/0bc6xg52swj6b2i-ir0ry

VertexShapeFunction can be combined with VertexSize:

https://wolfram.com/xid/0bc6xg52swj6b2i-e414xo

VertexShapeFunction has higher priority than VertexShape:

https://wolfram.com/xid/0bc6xg52swj6b2i-lnnzsy

VertexSize (7)
By default, the size of vertices is computed automatically:

https://wolfram.com/xid/0bc6xg52swj6b2i-dsy1ve

Specify the size of all vertices using symbolic vertex size:

https://wolfram.com/xid/0bc6xg52swj6b2i-lskxsr

Use a fraction of the minimum distance between vertex coordinates:

https://wolfram.com/xid/0bc6xg52swj6b2i-3lxk1

Use a fraction of the overall diagonal for all vertex coordinates:

https://wolfram.com/xid/0bc6xg52swj6b2i-my5omo

Specify size in both the and
directions:

https://wolfram.com/xid/0bc6xg52swj6b2i-c7twgs

Specify the size for individual vertices:

https://wolfram.com/xid/0bc6xg52swj6b2i-h6r4ja

VertexSize can be combined with VertexShapeFunction:

https://wolfram.com/xid/0bc6xg52swj6b2i-b3jw4t

VertexStyle (4)

https://wolfram.com/xid/0bc6xg52swj6b2i-ehbi7i


https://wolfram.com/xid/0bc6xg52swj6b2i-dtkst6

VertexShapeFunction can be combined with VertexStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-om30z

https://wolfram.com/xid/0bc6xg52swj6b2i-nnfnwx

VertexShapeFunction has higher priority than VertexStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-kfv4n

https://wolfram.com/xid/0bc6xg52swj6b2i-cldcke

VertexStyle can be combined with BaseStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-bby1h9

VertexStyle has higher priority than BaseStyle:

https://wolfram.com/xid/0bc6xg52swj6b2i-d0df6

VertexWeight (3)
Set the weight for all vertices:

https://wolfram.com/xid/0bc6xg52swj6b2i-coy9ti


https://wolfram.com/xid/0bc6xg52swj6b2i-jjkrix

Specify the weight for individual vertices:

https://wolfram.com/xid/0bc6xg52swj6b2i-b1lkq5


https://wolfram.com/xid/0bc6xg52swj6b2i-li3iht

Use any numeric expression as a weight:

https://wolfram.com/xid/0bc6xg52swj6b2i-lxjpz1


https://wolfram.com/xid/0bc6xg52swj6b2i-ite8vv

Applications (11)Sample problems that can be solved with this function
Basic Applications (7)

https://wolfram.com/xid/0bc6xg52swj6b2i-oba674

Style vertices and edges of a buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-ji7zqg

Annotate vertices and edges of a buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-ppixl

https://wolfram.com/xid/0bc6xg52swj6b2i-xodvq1


https://wolfram.com/xid/0bc6xg52swj6b2i-7vfk0s

Modify a buckyball graph parameters:

https://wolfram.com/xid/0bc6xg52swj6b2i-8xu4xp


https://wolfram.com/xid/0bc6xg52swj6b2i-9fwthq


https://wolfram.com/xid/0bc6xg52swj6b2i-05o64l

Generate a buckyball graph represented as a 2D plot:

https://wolfram.com/xid/0bc6xg52swj6b2i-zmdool

Basic properties of the class 1 buckyball graph; the number of vertices:

https://wolfram.com/xid/0bc6xg52swj6b2i-lcolir


https://wolfram.com/xid/0bc6xg52swj6b2i-uqxem7

Basic properties of the class 2 buckyball graph; the number of vertices:

https://wolfram.com/xid/0bc6xg52swj6b2i-4jocuw


https://wolfram.com/xid/0bc6xg52swj6b2i-tobqkt

Graph Theory (4)
Assign distinct colors to adjacent vertices of a buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-4jz52

https://wolfram.com/xid/0bc6xg52swj6b2i-kxwmt3


https://wolfram.com/xid/0bc6xg52swj6b2i-b4fkus

Assign distinct colors to adjacent edges of a buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-s48ogv

https://wolfram.com/xid/0bc6xg52swj6b2i-cqc1uy


https://wolfram.com/xid/0bc6xg52swj6b2i-1rqn74

Find the shortest tour in a buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-3gl0mt

https://wolfram.com/xid/0bc6xg52swj6b2i-uud6n9


https://wolfram.com/xid/0bc6xg52swj6b2i-d3j6vr

Find a spanning tree in a buckyball graph:

https://wolfram.com/xid/0bc6xg52swj6b2i-e7nzw7

https://wolfram.com/xid/0bc6xg52swj6b2i-zz53rg

https://wolfram.com/xid/0bc6xg52swj6b2i-rugbpc

Properties & Relations (2)Properties of the function, and connections to other functions
The ratio of the number of vertices to the number of edges is :

https://wolfram.com/xid/0bc6xg52swj6b2i-01h6xe


https://wolfram.com/xid/0bc6xg52swj6b2i-k74xgz

BuckyballGraph[1] is the graph corresponding to the truncated icosahedron:

https://wolfram.com/xid/0bc6xg52swj6b2i-wefvfg


https://wolfram.com/xid/0bc6xg52swj6b2i-yt45p6


https://wolfram.com/xid/0bc6xg52swj6b2i-oeumfp

Wolfram Research (2022), BuckyballGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/BuckyballGraph.html.
Text
Wolfram Research (2022), BuckyballGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/BuckyballGraph.html.
Wolfram Research (2022), BuckyballGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/BuckyballGraph.html.
CMS
Wolfram Language. 2022. "BuckyballGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BuckyballGraph.html.
Wolfram Language. 2022. "BuckyballGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BuckyballGraph.html.
APA
Wolfram Language. (2022). BuckyballGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BuckyballGraph.html
Wolfram Language. (2022). BuckyballGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BuckyballGraph.html
BibTeX
@misc{reference.wolfram_2025_buckyballgraph, author="Wolfram Research", title="{BuckyballGraph}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/BuckyballGraph.html}", note=[Accessed: 29-March-2025
]}
BibLaTeX
@online{reference.wolfram_2025_buckyballgraph, organization={Wolfram Research}, title={BuckyballGraph}, year={2022}, url={https://reference.wolfram.com/language/ref/BuckyballGraph.html}, note=[Accessed: 29-March-2025
]}