WOLFRAM

BuckyballGraph
BuckyballGraph

gives the buckyball graph.

gives the ordern buckyball graph.

BuckyballGraph[n,"class"]

gives the ordern buckyball graph of class "class".

Details and Options

Examples

open allclose all

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

The buckyball graph:

Out[1]=1

Generate a class I, order-3 buckyball graph:

Out[1]=1

A class II, order-3 buckyball graph:

Out[2]=2

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

The buckyball graph:

Out[1]=1

Generate a class II, order-1 buckyball graph:

Out[1]=1

Generate a class I, order-3 buckyball graph:

Out[1]=1

A class II, order-3 buckyball graph:

Out[2]=2

Generate a directed buckyball graph:

Out[1]=1

Options  (77)Common values & functionality for each option

AnnotationRules  (3)

Specify an annotation for vertices:

Out[1]=1

Edges:

Out[1]=1

Graph itself:

Out[1]=1
Out[2]=2

DirectedEdges  (1)

By default, an undirected graph is generated:

Out[1]=1

Use DirectedEdges->True to generate a directed graph:

Out[2]=2

EdgeLabels  (7)

Label the edge 12:

Out[1]=1

Label all edges individually:

Out[2]=2

Use any expression as a label:

Out[1]=1

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

Out[1]=1

Use explicit coordinates to place labels:

Out[1]=1

Vary positions within the label:

Out[2]=2

Place multiple labels using Placed in a wrapper:

Out[1]=1

Any number of labels can be used:

Out[2]=2

Place multiple labels using EdgeLabels:

Out[3]=3

Use automatic labeling by values through Tooltip and StatusArea:

Out[1]=1

EdgeShapeFunction  (6)

Get a list of built-in settings for EdgeShapeFunction:

Out[1]=1

Undirected edges including the basic line:

Out[1]=1

Lines with different glyphs on the edges:

Out[2]=2

Directed edges including solid arrows:

Out[1]=1

Line arrows:

Out[2]=2

Open arrows:

Out[3]=3

Specify an edge function for an individual edge:

Out[1]=1

Combine with a different default edge function:

Out[2]=2

Draw edges by running a program:

Out[2]=2

EdgeShapeFunction can be combined with EdgeStyle:

Out[1]=1

EdgeShapeFunction has higher priority than EdgeStyle:

Out[2]=2

EdgeStyle  (4)

Style all edges:

Out[1]=1

Style individual edges:

Out[1]=1

EdgeStyle can be combined with EdgeShapeFunction:

Out[2]=2

EdgeShapeFunction has higher priority than EdgeStyle:

Out[4]=4

EdgeStyle can be combined with BaseStyle:

Out[1]=1

EdgeStyle has higher priority than BaseStyle:

Out[2]=2

EdgeWeight  (3)

Specify a weight for all edges:

Out[1]=1

Use any numeric expression as a weight:

Out[1]=1

Specify weights for individual edges:

Out[1]=1
Out[2]=2

GraphHighlight  (3)

Highlight the vertex 1:

Out[1]=1

Highlight the edge 12:

Out[1]=1

Highlight vertices and edges:

Out[1]=1

GraphLayout  (5)

By default, the layout is chosen automatically:

Out[1]=1

Specify layouts on special curves:

Out[1]=1

Specify layouts that satisfy optimality criteria:

Out[1]=1

VertexCoordinates overrides GraphLayout coordinates:

Out[1]=1

Use AbsoluteOptions to extract VertexCoordinates computed using a layout algorithm:

Out[1]=1
Out[2]=2

PlotTheme  (4)

Base Themes  (2)

Use a common base theme:

Out[1]=1

Use a monochrome theme:

Out[1]=1

Feature Themes  (2)

Use a large graph theme:

Out[1]=1

Use a classic diagram theme:

Out[1]=1

VertexCoordinates  (3)

By default, any vertex coordinates are computed automatically:

Out[1]=1

Extract the resulting vertex coordinates using AbsoluteOptions:

Out[2]=2

Specify a layout function along an ellipse:

Out[2]=2

Use it to generate vertex coordinates for a graph:

Out[3]=3

VertexCoordinates has higher priority than GraphLayout:

Out[1]=1

VertexLabels  (13)

Use vertex names as labels:

Out[1]=1

Label individual vertices:

Out[1]=1

Label all vertices:

Out[1]=1

Use any expression as a label:

Out[1]=1

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

Out[1]=1

Symbolic outside corner positions:

Out[2]=2

Symbolic inside positions:

Out[1]=1

Symbolic inside corner positions:

Out[2]=2

Use explicit coordinates to place the center of labels:

Out[1]=1

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

Out[1]=1

Place multiple labels:

Out[1]=1

Any number of labels can be used:

Out[2]=2

Use the argument to Placed to control formatting including Tooltip:

Out[1]=1

Or StatusArea:

Out[2]=2

Use more elaborate formatting functions:

Out[2]=2
Out[4]=4
Out[6]=6

VertexShapeFunction  (11)

Get a list of built-in collections for VertexShapeFunction:

Out[1]=1

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

Out[1]=1

Simple basic shapes:

Out[2]=2

Common basic shapes:

Out[3]=3

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

Out[1]=1
Out[2]=2

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

Out[1]=1
Out[2]=2

Draw individual vertices:

Out[1]=1

Combine with a default vertex function:

Out[2]=2

Draw vertices using a predefined graphic:

Out[1]=1

Draw vertices by running a program:

Out[2]=2

VertexShapeFunction can be combined with VertexStyle:

Out[1]=1

VertexShapeFunction has higher priority than VertexStyle:

Out[2]=2

VertexShapeFunction can be combined with VertexSize:

Out[1]=1

VertexShapeFunction has higher priority than VertexShape:

Out[1]=1

VertexSize  (7)

By default, the size of vertices is computed automatically:

Out[1]=1

Specify the size of all vertices using symbolic vertex size:

Out[1]=1

Use a fraction of the minimum distance between vertex coordinates:

Out[1]=1

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

Out[1]=1

Specify size in both the and directions:

Out[1]=1

Specify the size for individual vertices:

Out[1]=1

VertexSize can be combined with VertexShapeFunction:

Out[1]=1

VertexStyle  (4)

Style all vertices:

Out[1]=1

Style individual vertices:

Out[1]=1

VertexShapeFunction can be combined with VertexStyle:

Out[2]=2

VertexShapeFunction has higher priority than VertexStyle:

Out[4]=4

VertexStyle can be combined with BaseStyle:

Out[1]=1

VertexStyle has higher priority than BaseStyle:

Out[2]=2

VertexWeight  (3)

Set the weight for all vertices:

Out[1]=1
Out[2]=2

Specify the weight for individual vertices:

Out[1]=1
Out[2]=2

Use any numeric expression as a weight:

Out[1]=1
Out[2]=2

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

Basic Applications  (7)

Visualize a buckyball graph:

Out[1]=1

Style vertices and edges of a buckyball graph:

Out[1]=1

Annotate vertices and edges of a buckyball graph:

Label a vertex:

Out[2]=2

Style an edge:

Out[3]=3

Modify a buckyball graph parameters:

Out[1]=1

Layout:

Out[2]=2

Edge style:

Out[3]=3

Generate a buckyball graph represented as a 2D plot:

Out[1]=1

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

Out[1]=1

The number of edges:

Out[2]=2

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

Out[1]=1

The number of edges:

Out[2]=2

Graph Theory  (4)

Assign distinct colors to adjacent vertices of a buckyball graph:

Out[2]=2

Visualize the graph:

Out[3]=3

Assign distinct colors to adjacent edges of a buckyball graph:

Out[2]=2

Visualize the graph:

Out[3]=3

Find the shortest tour in a buckyball graph:

Out[2]=2

Highlight the tour:

Out[3]=3

Find a spanning tree in a buckyball graph:

Highlight the tour:

Out[3]=3

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 :

Out[1]=1
Out[2]=2

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

Out[1]=1
Out[2]=2
Out[3]=3

Interactive Examples  (1)Examples with interactive outputs

Animate by continuously changing the value of order n:

Out[2]=2
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.

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 ]}

@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 ]}

@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 ]}