Zonohedrification
Posted: Tue Jun 16, 2015 7:09 am
Hi
By way of introduction, I recently purchased Great Stella and am absolutely blown away by its capabilities, and by the highly professional way in which it has been designed and presented - I find the user interface generally makes the software very easy to use, even for a newcomer like myself. I bought Great Stella primarily as a tool to assist me with my prime interest, which is in making polyhedral models using modular origami. I definitely would not class myself as a mathematician although along the way have picked up a working knowledge of some of the basic maths underpinning polyhedra.
I recently discovered Zonohedra/Zonish polyhedra, and one of my many aims with Great Stella is to use it to generate Zonohedra which I can then replicate using Origami (sorry Rob, no plans to use your nets at this stage, although I might be tempted with some models that can't be constructed using my preferred modular origami).
I've now spent some time using Great Stella to generate a number of Zonohedra/Zonish polyhedra. Brilliant!
I've been using George Hart's website as a reference point, which I've found particularly useful in gaining some understanding of the principles involved.
However I now have a few questions:
1) George Hart on his Zonish Polyhedra page - see http://www.georgehart.com/virtual-polyh ... hedra.html, refers to the use of an icosidodecahedron as a seed to produce various polyhedra, starting with the addition of one zone,then two etc. Addition of a third zone produces two results - an oblate and a prolate version. Great Stella generates the oblate version, but I can't find a way to generate the prolate version. Can it be done and if so , how?
As an aside George Hart has made these into a couple of sculptures - see http://www.georgehart.com/sculpture/fat-and-skinny.html.
2) My second question relates to a massive Zonohedron that George Hart shows at the bottom of his Zonohedrification page -see http://www.georgehart.com/virtual-polyh ... ation.html. He states that it is a 24 zone solid based on the truncated cuboctahedron. However the latter only has 13 zones, so I presume I need to further populate my "star" using some combination of vertices, edges or faces. But what combination? And how do I determine what combination to use?
3) Finally, I have now generated so many different Zonohedra/Zonish polyhedra that I badly need some form of numbering or naming system so that I can keep them organised and readily accessible. I don't want to reinvent the wheel, but my limited research to date has failed to reveal any commonly used system. Is there such a thing?
I would really welcome some help, so if anyone has any experience in using the Zonohedrify function and could share their knowledge, or can point me in the direction of any material that might help that would be very useful.
Thanks in advance
By way of introduction, I recently purchased Great Stella and am absolutely blown away by its capabilities, and by the highly professional way in which it has been designed and presented - I find the user interface generally makes the software very easy to use, even for a newcomer like myself. I bought Great Stella primarily as a tool to assist me with my prime interest, which is in making polyhedral models using modular origami. I definitely would not class myself as a mathematician although along the way have picked up a working knowledge of some of the basic maths underpinning polyhedra.
I recently discovered Zonohedra/Zonish polyhedra, and one of my many aims with Great Stella is to use it to generate Zonohedra which I can then replicate using Origami (sorry Rob, no plans to use your nets at this stage, although I might be tempted with some models that can't be constructed using my preferred modular origami).
I've now spent some time using Great Stella to generate a number of Zonohedra/Zonish polyhedra. Brilliant!
I've been using George Hart's website as a reference point, which I've found particularly useful in gaining some understanding of the principles involved.
However I now have a few questions:
1) George Hart on his Zonish Polyhedra page - see http://www.georgehart.com/virtual-polyh ... hedra.html, refers to the use of an icosidodecahedron as a seed to produce various polyhedra, starting with the addition of one zone,then two etc. Addition of a third zone produces two results - an oblate and a prolate version. Great Stella generates the oblate version, but I can't find a way to generate the prolate version. Can it be done and if so , how?
As an aside George Hart has made these into a couple of sculptures - see http://www.georgehart.com/sculpture/fat-and-skinny.html.
2) My second question relates to a massive Zonohedron that George Hart shows at the bottom of his Zonohedrification page -see http://www.georgehart.com/virtual-polyh ... ation.html. He states that it is a 24 zone solid based on the truncated cuboctahedron. However the latter only has 13 zones, so I presume I need to further populate my "star" using some combination of vertices, edges or faces. But what combination? And how do I determine what combination to use?
3) Finally, I have now generated so many different Zonohedra/Zonish polyhedra that I badly need some form of numbering or naming system so that I can keep them organised and readily accessible. I don't want to reinvent the wheel, but my limited research to date has failed to reveal any commonly used system. Is there such a thing?
I would really welcome some help, so if anyone has any experience in using the Zonohedrify function and could share their knowledge, or can point me in the direction of any material that might help that would be very useful.
Thanks in advance