ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 16 Jun 2019 14:18:26 -0500Looking for stellation of polyhedrahttps://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/ 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
Sun, 03 Feb 2019 11:45:06 -0600https://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/Answer by jipilab for <p>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</p>
https://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/?answer=45333#post-id-45333Hi!
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/thematic_tutorials/geometry/polyhedra_quickref.html
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/chap15.pdf
Is the operation described in there?
Otherwise, please let us know what is the operation and we will add it to the desired methods.Tue, 05 Feb 2019 15:03:52 -0600https://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/?answer=45333#post-id-45333Comment by jipilab for <p>Hi!</p>
<p>Could give a precise definition of what you mean by stellation?</p>
<p>There is a quick reference page about things you can do with a polyhedron:</p>
<p><a href="https://doc.sagemath.org/html/en/thematic_tutorials/geometry/polyhedra_quickref.html">https://doc.sagemath.org/html/en/them...</a></p>
<p>Perhaps what you mean is related to the following methods. Say <code>P</code> is a polyhedron object then</p>
<ul>
<li><code>P.barycentric_subdivision()</code>: constructs a polyhedron out of <code>P</code> whose facets correspond to complete flags of faces of <code>P</code>.</li>
<li><code>P.stack(face)</code>: puts a new vertex a little bit outside of the face <code>face</code>.</li>
</ul>
<p>In general, Sage tries to follow the nomenclature presented in the Handbook of Discrete and Computational Geometry (Chapter 15):</p>
<p><a href="https://www.csun.edu/~ctoth/Handbook/chap15.pdf">https://www.csun.edu/~ctoth/Handbook/...</a></p>
<p>Is the operation described in there?</p>
<p>Otherwise, please let us know what is the operation and we will add it to the desired methods.</p>
https://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/?comment=46922#post-id-46922I 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"....Sun, 16 Jun 2019 14:18:26 -0500https://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/?comment=46922#post-id-46922Comment by PatB for <p>Hi!</p>
<p>Could give a precise definition of what you mean by stellation?</p>
<p>There is a quick reference page about things you can do with a polyhedron:</p>
<p><a href="https://doc.sagemath.org/html/en/thematic_tutorials/geometry/polyhedra_quickref.html">https://doc.sagemath.org/html/en/them...</a></p>
<p>Perhaps what you mean is related to the following methods. Say <code>P</code> is a polyhedron object then</p>
<ul>
<li><code>P.barycentric_subdivision()</code>: constructs a polyhedron out of <code>P</code> whose facets correspond to complete flags of faces of <code>P</code>.</li>
<li><code>P.stack(face)</code>: puts a new vertex a little bit outside of the face <code>face</code>.</li>
</ul>
<p>In general, Sage tries to follow the nomenclature presented in the Handbook of Discrete and Computational Geometry (Chapter 15):</p>
<p><a href="https://www.csun.edu/~ctoth/Handbook/chap15.pdf">https://www.csun.edu/~ctoth/Handbook/...</a></p>
<p>Is the operation described in there?</p>
<p>Otherwise, please let us know what is the operation and we will add it to the desired methods.</p>
https://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/?comment=45561#post-id-45561Hi
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/Stellation#Stellating_polyhedra
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/TriakisIcosahedron.html... Can we do that in sage?
PatWed, 27 Feb 2019 11:38:44 -0600https://ask.sagemath.org/question/45291/looking-for-stellation-of-polyhedra/?comment=45561#post-id-45561