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Looking for stellation of polyhedra

asked 2019-02-03 11:45:06 -0600

PatB gravatar image

Hi Sagists, I'm wondering if anyone knows a way to do stellation with the Polyhedron class? Mathematica has a Stellate function but they admit it is really an augment operation and not a true stellation thanks Pat Browne

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answered 2019-02-05 15:03:52 -0600

jipilab gravatar image

Hi!

Could give a precise definition of what you mean by stellation?

There is a quick reference page about things you can do with a polyhedron:

https://doc.sagemath.org/html/en/them...

Perhaps what you mean is related to the following methods. Say P is a polyhedron object then

  • P.barycentric_subdivision(): constructs a polyhedron out of P whose facets correspond to complete flags of faces of P.
  • P.stack(face): puts a new vertex a little bit outside of the face face.

In general, Sage tries to follow the nomenclature presented in the Handbook of Discrete and Computational Geometry (Chapter 15):

https://www.csun.edu/~ctoth/Handbook/...

Is the operation described in there?

Otherwise, please let us know what is the operation and we will add it to the desired methods.

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Hi Thanks for getting back to me. I'm looking to create various nets of stellations of the icosahedron as shown here for example: https://en.wikipedia.org/wiki/Stellat... I discovered this in Wenninger's book Polyhedron Models - number 27 shows the Second Stellation of the icosahedron - very beautiful. Mathworld shows the first stellated form of the isocasehdron the Triakis Icosahedron and provides a net for it http://mathworld.wolfram.com/TriakisI.... Can we do that in sage? Pat

PatB gravatar imagePatB ( 2019-02-27 11:38:44 -0600 )edit

I see. As of now, it is now possible to deal with these kinds of stellation of polytopes in Sage. Currently, it can only deal with convex shapes. Eventually, it is a long term goal to be able to deal with collections of polyhedral cells. But currently, it is not really supported as "1 object"....

jipilab gravatar imagejipilab ( 2019-06-16 14:18:26 -0600 )edit

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Asked: 2019-02-03 11:45:06 -0600

Seen: 57 times

Last updated: Feb 05