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As intro to a talk, I am looking for finite, simple, connected graphs (no loops, no multi-edges) used in arts and design.

This is a wide field and I would like to direct this a bit further; I believe I am looking for straight lines/ edges between vertices (no curved lines); I'm looking for natural 'embeddings' resulting in the relevant view (not stick figures that can be looked at as graphs)

Which other pieces of art should I consider? Any piece of art with the 'Frucht graph'?
Any interesting math or meaning in those? Or is this just geometry, some planar graphs, possibly playing with symmetries and patterns?

References

Examples of graphs

graph used in HSBC logo

Grid graph as per MS logo

graph used in Mitsubishi logo

Dürer's copper plate engraving

Tableau 1 PM

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There is whole web page about the spikey, the logo currently used by Wolfram.com, https://writings.stephenwolfram.com/2018/12/the-story-of-spikey/, which is apparently a projection of a rhombic hexecontahedron.

spikey

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This classical painting by Barbari from 1495 is in the public domain and shows a dodecahedron (20 vertices, 30 edges) and a rhombicuboctahedron (18 squares and 8 triangles). The wikipedia file is nicely annotated.

Portrait of Luca Pacioli

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The MAA logo, a regular icosahedron, https://upload.wikimedia.org/wikipedia/en/8/8c/Mathematical_Association_of_America_logo.svg

The Christian cross, and the Jewish star.

The letters A, E, F, H, I, K, L, M, N, T, V, W, X, Y, and Z.

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  • $\begingroup$ Hi Gerry, many thanks! I buy the MAA logo (it is clear what is meant...); the Christian cross (StarGraph[5]) and the Jewish star/ star of David ( GraphData[ "HexagramConfigurationGraph"]) work for me... letters can be considered 'design' in a wide view; some specific ones are: A is the GraphData["BullGraph"], B is the GridGraph[{3,2}], D and O could be done as a 4-cycle, H is the GraphData["HGraph"], I is an n-path, P is the GraphData["BannerGraph"], R is the GraphData["RGraph"], X is the cross/ 5-star, Y is the 4-star (fits better than T)... $\endgroup$ Commented Mar 30 at 11:20
  • $\begingroup$ I find some of the other letters a bit difficult, e.g., Z and W as graphs are both paths and only 'work' with specific choices of angel between the 2 edges at a vertex. $\endgroup$ Commented Mar 30 at 11:22
  • $\begingroup$ Actually, in addition to the 5-star, there is also another cross graph with one 'longer leg': GraphData["CrossGraph"] $\endgroup$ Commented Mar 30 at 12:30
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    $\begingroup$ I didn't mention B, D, O, P, and R because you specified, "no curved lines". $\endgroup$ Commented Mar 30 at 21:12
  • $\begingroup$ Agree, P is easier to recognize than R in standard embeddings and O is easier than D... ;-) BTW: The logos of math institutes seems to be a category in its own. Many thanks! $\endgroup$ Commented Mar 31 at 7:57
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Various artists like Escher use graphs. One is Michael Cheshire.

hexagonal grid on wood

Another is Rinus Roelofs.

plastic sculpture

Ravensbourne University expands the Hirschhorn Medallion.

Ravensbourne

One set of graph-like objects in art are the Lesser Keys of Solomon.

enter image description here

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This graph is used in the logo of Alcoa since 1963

alcoa logo

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  • $\begingroup$ The Arconic logo (Alcoa spin-off) is a variation of this with 11 vertices, it can be found at houseofgraphs.org/graphs/53163 and plays in an interesting way with 3d expectations vs 2d depiction $\endgroup$ Commented Apr 10 at 12:39
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ACE chemical co, an Australian chemicals wholesaler, has a logo based on the 'R graph'

r graph

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There is a graph that can be drawn in a way resembling the Louis Vuitton label

LV logo graph

It has 7 vertices and 6 edges...

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The BP logo can be looked at as a graph with 3 layers of 18 diamonds on a circular chain, has 90 vertices and 144 edges and a graph automorphism group of order 72.

graph

BP logo

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I like the Renault logo used 1992 to 2021.

It can be looked at as a 'Möbius strip with 2 half-twists'; topologically, that is a cylinder but an embedding in $\mathbb{R}^3$ can't be untwisted.

As a graph it is a 4-prism (without any twisting)

4 prism

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The Dresdener Bank logo (German bank acquired in 2009) had a logo based on an unnamed graph with 9 vertices and 12 edges. If you know it, you may not recognize it in standard embedding

enter image description here

but possibly with this re-shaping

HoG21054

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There is a painting by the French painter Paul Sérusier (died October 1927) that consists of floating tetrahedra.
It is called... well, 'Tétraèdres'.

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The AMD logo can be looked at as a graph though there may be some room to interpret this in different ways

enter image description here

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Very interesting designs, which from the graph point of view are just 'boring' n-cycles $C_n$, are the so-called pieces of TSP art by Robert Bosch and others:
you turn a desired picture into a patch of clustered points and then let a computer find a TSP-optimal path between them, as in the 'Mona Lisa'-inspired cycle below.

mona lisa as TSP art

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You can consider triangulations of 'every day' objects or maps/ country coordinates, e.g., boundaryPts = Map[Reverse, CountryData["Australia", "SchematicCoordinates"], {2}]; mesh = TriangulateMesh[Polygon[boundaryPts]]

Triangulation of Australia

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Many national flags can be looked at as graphs; and it feels like the the 3 bars or columns design is very frequent/ part of every other flag (aka GraphData[{"Ladder",4}])

3 bar design

Benin uses an interesting variation, Chile's flag looks different but the underlying graph is the same

enter image description here

Bhutan uses the diamond graph with a dragon.

Czech Republic's flag has a triangle and 2 squares

CR's flag

etc...

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  • $\begingroup$ There are countries with 3-ladders (e.g., Malta or Vatican city) and 5-ladders (e.g., Mauritius) $\endgroup$ Commented Apr 5 at 7:23
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    $\begingroup$ Your first two pictures are of different graphs. $\endgroup$ Commented Apr 7 at 12:51
  • $\begingroup$ @Rosie F, yes, agree; I believe the text says that... doesn't it? $\endgroup$ Commented Apr 7 at 13:28
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In terms of flags, one of the most interesting designs is the flag of Wiphala representing some native peoples of the Andes that include today's Bolivia, Peru, Chile, Ecuador, northwestern Argentina and southern Colombia.

It's the 8x8 grid graph with 7x7=49 fields

Wiphala flag

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