username5243 wrote:Interesting...
Would you mind sharing what all you have for this project so far at some point?
quickfur wrote:Depends. Images of what? The various things I referred to that are CRF may already have images posted somewhere on this forum; if you search for spidrox, for example, you'll probably find a few images I rendered. You can see projections of the grand antiprism on my website.
As far as the other (non-uniform) members of the grand antiprism family are concerned, sorry, no, I don't have images of those. But once you understand the grand antiprism itself, it's not hard to imagine the rest of them in your mind's eye.
student91 wrote:Don't forget this post of Quickfur's.
Klitzing wrote:[...]
(Quickfur too has an according link to a special spidrox page within his CRF section,
but sadly that link does not work...)[...]
quickfur wrote:This is a very crude rendering, but I managed to construct a 5-5 duoprismatic compound swirl:
I didn't realize this before, but this construction scheme is very neat, in that the vertices should(?) be transitive, so one ought to be able to take the dual and get a cell-transitive polychoron. I particularly like how as the parameters increase, the shape starts to approach one of Bower's polytwisters. (Probably not a regular polytwister, but I think it should qualify as a uniform polytwister.)
Very nice construction!
Mercurial, the Spectre wrote:quickfur wrote:This is a very crude rendering, but I managed to construct a 5-5 duoprismatic compound swirl:
[...]
I wonder what its dual would look like.
quickfur wrote:Mercurial, the Spectre wrote:quickfur wrote:This is a very crude rendering, but I managed to construct a 5-5 duoprismatic compound swirl:
[...]
I wonder what its dual would look like.
Apparently, it's a very nice skew tegum! Here's a render with two randomly-picked cells highlighted:
If you look carefully, you can see how these cells stack on each other forming a twisting, spiralling column wrapping around the two orthogonal great circles of the tegum.
The cells themselves are elongated lemon-like shapes which are twisted by 90°, joining one great circle to the other.
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