References to finite, simple, connected graphs (no loops, no multi-edges) used in arts and design

Question

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)

rather not: a painting of the pyramids of Giza - the pyramids have to have some shape
rather not: the Nike logo, for me, only works with volume not just as a tick mark and the tick mark only works with a defined angle which comes out of nowhere
rather not: the Chanel logo has curved lines and a loop and replacing that with additional vertices and edges, e.g., a square, destroys the logo
rather not: Penck's stick figure paintings - start from https://en.wikipedia.org/wiki/A._R._Penck#Works
OKish: Paul Klee's grid format compositions - see https://www.artsoullifemagazine.com/paul-klee-a-symphony-of-colors-and-shapes
OKish: Dali's last supper set within a transparent dodecahedron or twelve-sided space as perceived in the pentagon-shaped windowpanes behind the table - see https://en.wikipedia.org/wiki/The_Sacrament_of_the_Last_Supper
OKish: tilings, though somehow, in many cases they are meant to appear infinite which does not fit to what I am looking for
OKish: the tableau painting of Piet Mondrian - see example below
OKish: the pyramids of Giza as a 'design statement'
spot on: the truncated rhombohedron in Dürer's copper plate engraving Melencolia I - see https://en.wikipedia.org/wiki/Mathematics_and_art#/media/File:D%C3%BCrer_Melancholia_I.jpg
spot on: the Microsoft logo - see https://houseofgraphs.org/graphs/52391
spot on: the HSBC logo - see https://houseofgraphs.org/graphs/51299
spot on: the Mitsubishi logo - https://houseofgraphs.org/graphs/53155

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

This is on the nerdy side of things... https://hanusadesign.com/collections/a-dash-of-color/products/forbidden-subgraph-earrings-nylon — Michael T, Mar 29 '25 at 15:44
There is a beautiful article at https://publicdomainreview.org/essay/polyhedral-perspective/ called 'The Polyhedral Perspective' by Noam Andrews that describes how in the Renaissance geometrical solids were being included in art/ paintings: many examples! — Michael T, Mar 30 '25 at 07:40

score 2 · Answer 1 · answered Apr 07 '25 at 11:56

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.

Reference

https://mathworld.wolfram.com/RhombicHexecontahedron.html

score 1 · Answer 2 · answered Mar 30 '25 at 07:50

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.

References

score 1 · Answer 3 · answered Mar 30 '25 at 10:15

1

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.

answered Mar 30 '25 at 10:15

Gerry Myerson

185,413

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)... – Michael T Mar 30 '25 at 11:20
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. – Michael T Mar 30 '25 at 11:22
Actually, in addition to the 5-star, there is also another cross graph with one 'longer leg': GraphData["CrossGraph"] – Michael T Mar 30 '25 at 12:30
1

I didn't mention B, D, O, P, and R because you specified, "no curved lines". – Gerry Myerson Mar 30 '25 at 21:12
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! – Michael T Mar 31 '25 at 07:57

score 1 · Answer 4 · answered Apr 03 '25 at 16:27

1

Various artists like Escher use graphs. One is Michael Cheshire.

Another is Rinus Roelofs.

Ravensbourne University expands the Hirschhorn Medallion.

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

answered Apr 03 '25 at 16:27

Ed Pegg

21,868

score 1 · Answer 5 · answered Apr 09 '25 at 06:09

1

This graph is used in the logo of Alcoa since 1963

References

answered Apr 09 '25 at 06:09

Michael T

1,742

The Arconic logo (Alcoa spin-off) is a variation of this with 11 vertices, it can be found at https://houseofgraphs.org/graphs/53163 and plays in an interesting way with 3d expectations vs 2d depiction – Michael T Apr 10 '25 at 12:39

score 1 · Answer 6 · answered Apr 19 '25 at 13:00

1

ACE chemical co, an Australian chemicals wholesaler, has a logo based on the 'R graph'

References

https://www.acechem.com.au/

answered Apr 19 '25 at 13:00

Michael T

1,742

score 1 · Answer 7 · answered Apr 19 '25 at 14:28

1

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

It has 7 vertices and 6 edges...

References

https://houseofgraphs.org/graphs/616

answered Apr 19 '25 at 14:28

Michael T

1,742

score 1 · Answer 8 · answered May 19 '25 at 09:38

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.

References

https://houseofgraphs.org/graphs/53179
GraphUnion[Flatten[Table[{UndirectedEdge[{k,k2},{Mod[k-1,18,1],k2+1}],UndirectedEdge[{k,k2},{k,k2+1}] }, {k,1,18},{k2,1,4}],2]]

score 0 · Answer 9 · answered Mar 30 '25 at 06:49

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)

Reference

score 0 · Answer 10 · answered Mar 30 '25 at 07:08

0

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

but possibly with this re-shaping

References

answered Mar 30 '25 at 07:08

Michael T

1,742

The Deutsche Bank logo (https://www.db.com/news/detail/20240423-this-way-for-modern-banking-deutsche-bank-logo-turns-50?language_id=1) can be looked at as a diamond graph: https://houseofgraphs.org/graphs/28 – Michael T Apr 13 '25 at 15:20
Jenapharm has a logo that is based on a similar graph (with an additional vertex in each of the 3 corners) https://houseofgraphs.org/graphs/53166 – Michael T Apr 19 '25 at 12:56

score 0 · Answer 11 · answered Mar 30 '25 at 07:38

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

References

score 0 · Answer 12 · answered Apr 02 '25 at 06:40

0

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

References

answered Apr 02 '25 at 06:40

Michael T

1,742

Michael T · Answer 13 · 2025-05-19T10:41:02.163

0

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}])

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

Bhutan uses the diamond graph with a dragon.

Czech Republic's flag has a triangle and 2 squares

etc...

References

edited May 19 '25 at 10:41

answered Apr 04 '25 at 15:53

Michael T

1,742

There are countries with 3-ladders (e.g., Malta or Vatican city) and 5-ladders (e.g., Mauritius) – Michael T Apr 05 '25 at 07:23
1

Your first two pictures are of different graphs. – Rosie F Apr 07 '25 at 12:51
@Rosie F, yes, agree; I believe the text says that... doesn't it? – Michael T Apr 07 '25 at 13:28

Michael T · Answer 14 · 2025-04-05T09:46:36.120

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.

References

score 0 · Answer 15 · answered Apr 06 '25 at 08:09

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]]

Reference

Mathematica is available for free behind a registration wall at https://www.wolframcloud.com/

score -1 · Answer 16 · answered Apr 05 '25 at 07:27

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

References

https://commons.wikimedia.org/w/index.php?curid=988731

References to finite, simple, connected graphs (no loops, no multi-edges) used in arts and design

16 Answers16