TOPICS
Search

Erected Polygon Graph


ErectedPolygonGraphs

The term (n,k)-erected polygon graph is a term adopted in this work to describe the graph on n(k-1) vertices obtained by erecting k-gons on the sides of a central n-gon. A number of cases are illustrated above.

The special case (n,k)=(3,3) corresponds to the 2-triangular grid graph and the case (n,k)=(4,4) corresponds to the x-pentomino.

ErectedPolygonGraphsCircularEmbeddings

The (n,k)-erected polygon graph can be given a circular n(k-1)-gonal embedding with an embedded regular n-gon, as illustrated above.

ErectedPolygonGraphDresdenerBank

The (3,4)-erected polygon graph is illustrated above in several embeddings. The third of these corresponds to the logo of Dresdener Bank (Michael T, 2025).

ContractedErectedPolygonGraphs

In some cases, such as those illustrated above, vertices of erected regular polygons coincide.

Erected polygon graphs are unit-distance by construction.


See also

Polygon, Regular Polygon, Tiling

Explore with Wolfram|Alpha

References

Michael T. "References to Finite, Simple, Connected Graphs (No Loops, No Multi-Edges) Used in Arts and Design." https://math.stackexchange.com/q/5051205. Mar. 30, 2025.

Cite this as:

Weisstein, Eric W. "Erected Polygon Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ErectedPolygonGraph.html

Subject classifications