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I am trying to generate the Petrie polygon projection of the 8-cube in Mathematica, like this one:

enter image description here

I tried using, for example, the HypercubeGraph function:

HypercubeGraph[8]

which generates

enter image description here

As you can tell from the lack of symmetry (notice the shape of the innermost ring, for example), this is not the right projection. I also tried looking at some GraphPlot options like Method:

GraphPlot[HypercubeGraph[8], Method -> "SpringElectricalEmbedding"]

but to no avail. How can I generate the Petrie polygon projection of an 8-cube in Mathematica?

share|improve this question
up vote 10 down vote accepted

As I understand this, GraphData are based on many nice custom pre-set layouts. Graph is based on algorithms that compute layouts, so computation is not always guaranteed to result in a specially defined geometry.

SetProperty[GraphData[{"Hypercube", 8}], VertexStyle -> Red]

enter image description here

share|improve this answer
    
Thank you! Is there a way to label different vertices or color them differently according to a function? – Carlos Feb 23 at 0:20
    
@user1667423 VertexShapeFunction most generally with. You should take a good nickname. – Vitaliy Kaurov Feb 23 at 0:31
    
Thanks again! It doesn't seem like the projection is working properly for the 3-cube. Is it not currently possible to specify the Petrie projection in general? – Carlos Feb 23 at 1:12

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