Berman-Gévay-Pisanski Configuration

Author

Eric W. Weisstein
July 31, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/Configurations/Berman-Gevay-PisanskiConfiguration.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/Berman-Gevay-PisanskiConfiguration.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Sources

Sources: L. W. Berman, G. Gevay, and T. Pisanski, On a New (21_4) Polycyclic Configuration, Electronic Journal of Combinatorics 31 (2024), P4.54, https://doi.org/10.37236/12405; https://arxiv.org/abs/2309.12992

Configuration data

Exact affine coordinates from the attached source notebook are stored as homogeneous projective coordinates {x,y,1}.

points={{0,2},{(Sqrt[3]),-1},{-(Sqrt[3]),-1},{,-1},{,},{,},{,},{,},{,-1},{,},{,},{,},{,},{,},{,},{,},{,},{,},{,},{,},{,}};
lines={{1,2,8,6},{1,3,5,7},{1,4,10,14},{1,9,18,19},{2,3,9,4},{2,5,11,15},{2,7,16,20},{3,6,12,13},{3,8,17,21},{4,18,16,11},{4,21,20,12},{5,19,21,10},{5,16,17,12},{6,17,18,10},{6,20,19,11},{7,11,14,13},{7,19,17,15},{8,12,15,14},{8,20,18,13},{9,10,13,15},{9,21,16,14}};

ConfigurationNotation[lines]

ConfigurationDiagram[points,lines,VertexLabels->None]

g=ConfigurationGraph[points,lines,VertexLabels->Automatic]

EdgeList[g]

LeviGraph[incidence]//RecognizeGraph

GraphData

GraphDataString

file=OpenWrite["~/configs.m"]

WriteString[
file,
GraphDataString[
,
"StandardName"->"BermanGevayPisanskiConfigurationGraph",
"Name"->"Berman-Gévay-Pisanski configuration graph",
"Classes"->{"Configuration"},
"IncidenceLines"->{
{{1,2,8,6},{1,3,5,7},{1,4,10,14},{1,9,18,19},{2,3,9,4},{2,5,11,15},{2,7,16,20},{3,6,12,13},{3,8,17,21},{4,18,16,11},{4,21,20,12},{5,19,21,10},{5,16,17,12},{6,17,18,10},{6,20,19,11},{7,11,14,13},{7,19,17,15},{8,12,15,14},{8,20,18,13},{9,10,13,15},{9,21,16,14}}
},
"Information"->"Berman-Gevay-PisanskiConfigurationGraph"
]
]

Close[file]