Quickfur's renders

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Re: Quickfur's renders

Postby quickfur » Tue May 01, 2018 8:10 pm

This month's Polytope of the Month is the runcinated snub 24-cell:

Image

Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox. Some of my favorite renders:

Image

(showing the pyritohedral symmetry of the cupolae)

Image

(showing the cells that lie on the projection envelope).
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Re: Quickfur's renders

Postby username5243 » Tue May 01, 2018 11:03 pm

quickfur wrote:Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox.


Actually, there's one more convex scaliform polytope you haven't posted yet - tutcup (truncated tetrahedral cupolipirsm), which has 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae. It is a segmentotope whose bases are two oppositely oriented truncated tetrahedra.
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Re: Quickfur's renders

Postby quickfur » Tue May 01, 2018 11:40 pm

username5243 wrote:
quickfur wrote:Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox.


Actually, there's one more convex scaliform polytope you haven't posted yet - tutcup (truncated tetrahedral cupolipirsm), which has 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae. It is a segmentotope whose bases are two oppositely oriented truncated tetrahedra.

Ooh! Thanks for the tip! I'll be sure to post that next month! :lol: :nod:

Are all of the convex scaliforms already known? Or are these only the currently-known ones?
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Re: Quickfur's renders

Postby Mercurial, the Spectre » Fri May 11, 2018 5:01 pm

quickfur wrote:
username5243 wrote:
quickfur wrote:Nothing new here, but this is the last of the known scaliform polychora on my website, so it seems like a natural thing to follow after spidrox.


Actually, there's one more convex scaliform polytope you haven't posted yet - tutcup (truncated tetrahedral cupolipirsm), which has 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae. It is a segmentotope whose bases are two oppositely oriented truncated tetrahedra.

Ooh! Thanks for the tip! I'll be sure to post that next month! :lol: :nod:

Are all of the convex scaliforms already known? Or are these only the currently-known ones?

Definitely yes in 4D. They are related to a specific convex uniform polychoron (ex. tutcup-sircope, bidex-ex, and prissi-prico).
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Re: Quickfur's renders

Postby quickfur » Fri May 11, 2018 6:28 pm

Not sure I understand. Are you saying we know all of them, or these are the only ones we know of? If the former, do we have proof that there are no others?
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Re: Quickfur's renders

Postby quickfur » Tue May 15, 2018 12:13 am

Anyways, in the meantime, I've been adding the Johnson solids to my website, and today came to J32, which is an EKF of the icosahedron. So I made an animation of it:

Image

I know you guys have been asking for this for a long time... :oops: well I finally got round to it. :nod:
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