Hi! I'm new here. I like polytopes, and stella program!
I have idea for 4D dual-morphing.
4D morph by truncation method is...
parent -> truncated -> rectified -> bitruncated -> rectified dual -> truncated dual -> dual
And, 4D morph by expension (morph with rectangles) method is...
parent -> expanded (in 4D, it also be runcination) -> dual
If you can't understand, see here.
[url]http://en.wikipedia.org/wiki/Uniform_po ... #Geometric derivations for 46 nonprismatic Wythoffian uniform polychora[/url]
4D Dual-morphing
- robertw
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I thought about 4D dual morphing before, but haven't got around to it yet. I guess all you'd be able to see during the morph is the 3D projection, ie not cross-sections or nets, though you could convert a morph to be the new base model to obtain those.
For morph by rectangles (maybe I should rename this morph by expansion?), we have the following:
Morph by truncation is trickier to do in a general way (ie not limited to uniform polytopes), as there is no rectified form in general, so I don't rely on that in 3D.
I'll probably look into it sometime.
Thanks,
Rob.
For morph by rectangles (maybe I should rename this morph by expansion?), we have the following:
- each vertex becomes a new small dual cell that grows
- each cell shrinks to nothing, becoming a dual vertex
- each edge becomes a long thin cell that grows wider and shorter till it becomes a dual face
- each face expands into a short prism that grows longer and thinner till it becomes a dual edge
Morph by truncation is trickier to do in a general way (ie not limited to uniform polytopes), as there is no rectified form in general, so I don't rely on that in 3D.
I'll probably look into it sometime.
Thanks,
Rob.