Modifications of the snub demitesseract

Discussion of known convex regular-faced polytopes, including the Johnson solids in 3D, and higher dimensions; and the discovery of new ones.

Modifications of the snub demitesseract

Postby quickfur » Wed Mar 26, 2014 5:38 pm

I'm wondering, is the vertex figure of the snub 24-cell (snub demitesseract ;)) a CRF tridiminished icosahedron? 'cos if it is, then wouldn't it imply that the truncated snub 24-cell and the rectified snub 24-cell must also be CRF, even though they are not uniform? And the Stott expansion would be CRF too (I believe this is prismatorhombato snub 24-cell?).
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Re: Johnsonian Polytopes

Postby Marek14 » Wed Mar 26, 2014 6:23 pm

quickfur wrote:I'm wondering, is the vertex figure of the snub 24-cell (snub demitesseract ;)) a CRF tridiminished icosahedron? 'cos if it is, then wouldn't it imply that the truncated snub 24-cell and the rectified snub 24-cell must also be CRF, even though they are not uniform? And the Stott expansion would be CRF too (I believe this is prismatorhombato snub 24-cell?).


Yes, of course it's CRF tridiminished icosahedron :)
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Re: Johnsonian Polytopes

Postby quickfur » Wed Mar 26, 2014 7:10 pm

I can't believe this CRF has been sitting under our noses all this time, and we never thought of it!! So, I did a Stott expansion on the snub 24-cell's edges, and produced the truncated snub 24-cell, confirmed to be CRF. Here's a mugshot of this new pretty:

Image

It has a very interesting structure where pairs of truncated tetrahedra (green) share an edge, interspersed by tridiminished icosahedra (brown) that apparently link things together in ... a 4D equivalent of pyritohedral symmetry? The yellow cell in the center is, of course, a truncated icosahedron (aka buckyball :P).

This beauty has 24 truncated icosahedra, 96 tridiminished icosahedra, and 120 truncated tetrahedra.

Edit: uploaded .def and .off files to the wiki page Truncated snub demitesseract.

Edit 2: Hmm, apparently I forgot about the tetrahedra of the second kind in the snub 24-cell, that produces analogous truncated tetrahedra in this CRF, that sits between 4 other truncated tetrahedra. :)
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Re: Johnsonian Polytopes

Postby student91 » Wed Mar 26, 2014 8:44 pm

quickfur wrote:I can't believe this CRF has been sitting under our noses all this time, and we never thought of it!![...]

That's not entirely true, it was already discovered. If you read all subsequent pages, you will read that it can be seen as an ico-diminished o5o3x3x. In fact every 120-uniform can have such a ico-diminishing if it allows a shallow cut. You've already listed the 120-uniforms with this property, in the "number of CRF's topic." Every such ico-diminishing can also be seen as a stott-expansion of the respective polytope, then you just apply the diminishing before you apply the expansion. This is all that gets, very long-windedly, explained in all the subsequent pages.
It has a very interesting structure where pairs of truncated tetrahedra (green) share an edge, interspersed by tridiminished icosahedra (brown) that apparently link things together in ... a 4D equivalent of pyritohedral symmetry? The yellow cell in the center is, of course, a truncated icosahedron (aka buckyball :P).
[...]
the symmetry is of course the snub 24-celll symmetry, maybe this symmetry is then more related to the pyritohedral symmetry than I thougt.
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Re: Johnsonian Polytopes

Postby quickfur » Wed Mar 26, 2014 8:58 pm

And of course, the rectified snub 24-cell is also CRF:

Image

It has 24 icosidodecahedra, 96 tridiminished icosahedra, 120 octahedra (divided into 24 octahedra which are surrounded only by other octahedra, and 96 octahedra that touch the icosidodecahedra).

Its coordinates are:
Code: Select all
apacs<0, 0, 2*phi, 2*phi^2>
apacs<1, 1, phi^3, phi^3>

epacs<0, phi^2, phi^3, 2+phi>
epacs<1, phi, 2*phi^2, phi^2>

I'll upload the software models to the wiki page: rectified snub demitesseract
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Re: Johnsonian Polytopes

Postby quickfur » Wed Mar 26, 2014 9:08 pm

student91 wrote:
quickfur wrote:I can't believe this CRF has been sitting under our noses all this time, and we never thought of it!![...]

That's not entirely true, it was already discovered. If you read all subsequent pages, you will read that it can be seen as an ico-diminished o5o3x3x. In fact every 120-uniform can have such a ico-diminishing if it allows a shallow cut. You've already listed the 120-uniforms with this property, in the "number of CRF's topic." Every such ico-diminishing can also be seen as a stott-expansion of the respective polytope, then you just apply the diminishing before you apply the expansion. This is all that gets, very long-windedly, explained in all the subsequent pages.
It has a very interesting structure where pairs of truncated tetrahedra (green) share an edge, interspersed by tridiminished icosahedra (brown) that apparently link things together in ... a 4D equivalent of pyritohedral symmetry? The yellow cell in the center is, of course, a truncated icosahedron (aka buckyball :P).
[...]
the symmetry is of course the snub 24-celll symmetry, maybe this symmetry is then more related to the pyritohedral symmetry than I thougt.

Haha, you're right. In fact, I may have unconsciously gotten the idea from your original post. :oops: But anyway, it's nice to finally have a model for it, with coordinates and nice renders. :P And I see that Klitzing has already posted the incmats for it, and for the rectified snub 24-cell.
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Re: Johnsonian Polytopes

Postby quickfur » Wed Mar 26, 2014 9:12 pm

And speaking of which, the rectified snub 24-cell looks suggestively like it can be bilbiro'd. If we take 6 icosidodecahedra lying on the same hyperplane (say the equator) and "squish" them into bilbiros, I think the rest of the structure should still remain mostly intact, and there's probably a way to make it CRF.
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Re: Johnsonian Polytopes

Postby quickfur » Wed Mar 26, 2014 9:23 pm

quickfur wrote:[..] In fact, I may have unconsciously gotten the idea from your original post.[...]

Argh... I think my memory is going with old age :( I actually replied to your original post that described these CRFs, can't believe I completely forgot!!! :oops: :oops: :oops:
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Re: Johnsonian Polytopes

Postby Klitzing » Wed Mar 26, 2014 11:06 pm

quickfur wrote:I'm wondering, is the vertex figure of the snub 24-cell (snub demitesseract ;)) a CRF tridiminished icosahedron? 'cos if it is, then wouldn't it imply that the truncated snub 24-cell and the rectified snub 24-cell must also be CRF, even though they are not uniform? And the Stott expansion would be CRF too (I believe this is prismatorhombato snub 24-cell?).


truncated sadi = tisadi (found in 2004 by Andrew Weimholt)
rectified sadi = risadi (found in 2004 by Andrew Weimholt)
Stott expanded sadi = prissi (found in 2005 by me)

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Re: Johnsonian Polytopes

Postby Klitzing » Wed Mar 26, 2014 11:14 pm

quickfur wrote:I can't believe this CRF has been sitting under our noses all this time, and we never thought of it!! So, I did a Stott expansion on the snub 24-cell's edges, and produced the truncated snub 24-cell, confirmed to be CRF. Here's a mugshot of this new pretty:

Image

It has a very interesting structure where pairs of truncated tetrahedra (green) share an edge, interspersed by tridiminished icosahedra (brown) that apparently link things together in ... a 4D equivalent of pyritohedral symmetry? The yellow cell in the center is, of course, a truncated icosahedron (aka buckyball :P).

This beauty has 24 truncated icosahedra, 96 tridiminished icosahedra, and 120 truncated tetrahedra.

Edit: uploaded .def and .off files to the wiki page Truncated snub demitesseract.

Edit 2: Hmm, apparently I forgot about the tetrahedra of the second kind in the snub 24-cell, that produces analogous truncated tetrahedra in this CRF, that sits between 4 other truncated tetrahedra. :)


There are no tetrahedra within tisadi!

Here is its long known matrix:
Code: Select all
288   *   * |   1   2   2   0   0   0 |  2  1   2   2   1  0  0 |  1  1  2  1  "head" of {5}
  * 288   * |   0   0   2   1   1   0 |  0  0   2   1   2  1  0 |  2  0  1  1  "arms" of {5}
  *   * 288 |   0   0   0   1   1   2 |  0  0   2   0   2  1  1 |  2  0  1  1  "legs" of {5}
------------+-------------------------+-------------------------+------------
  2   0   0 | 144   *   *   *   *   * |  2  0   2   0   0  0  0 |  1  1  2  0
  2   0   0 |   * 288   *   *   *   * |  1  1   0   1   0  0  0 |  0  1  1  1
  1   1   0 |   *   * 576   *   *   * |  0  0   1   1   1  0  0 |  1  0  1  1
  0   1   1 |   *   *   * 288   *   * |  0  0   0   0   2  1  0 |  2  0  0  1
  0   1   1 |   *   *   *   * 288   * |  0  0   2   0   0  1  0 |  2  0  1  0
  0   0   2 |   *   *   *   *   * 288 |  0  0   1   0   1  0  1 |  1  0  1  1
------------+-------------------------+-------------------------+------------
  6   0   0 |   3   3   0   0   0   0 | 96  *   *   *   *  *  * |  0  1  1  0
  3   0   0 |   0   3   0   0   0   0 |  * 96   *   *   *  *  * |  0  1  0  1
  2   2   2 |   1   0   2   0   2   1 |  *  * 288   *   *  *  * |  1  0  1  0
  2   1   0 |   0   1   2   0   0   0 |  *  *   * 288   *  *  * |  0  0  1  1
  1   2   2 |   0   0   2   2   0   1 |  *  *   *   * 288  *  * |  1  0  0  1
  0   3   3 |   0   0   0   3   3   0 |  *  *   *   *   * 96  * |  2  0  0  0
  0   0   3 |   0   0   0   0   0   3 |  *  *   *   *   *  * 96 |  0  0  1  1
------------+-------------------------+-------------------------+------------
 12  24  24 |   6   0  24  24  24  12 |  0  0  12   0  12  8  0 | 24  *  *  *  ti
 12   0   0 |   6  12   0   0   0   0 |  4  4   0   0   0  0  0 |  * 24  *  *  tut (full sym)
  6   3   3 |   3   3   6   0   3   3 |  1  0   3   3   0  0  1 |  *  * 96  *  tut (axial sym)
  3   3   3 |   0   3   6   3   0   3 |  0  1   0   3   3  0  1 |  *  *  * 96  teddi


--- rk
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Re: Johnsonian Polytopes

Postby Klitzing » Wed Mar 26, 2014 11:24 pm

quickfur wrote:And of course, the rectified snub 24-cell is also CRF:

Image

It has 24 icosidodecahedra, 96 tridiminished icosahedra, 120 octahedra (divided into 24 octahedra which are surrounded only by other octahedra, and 96 octahedra that touch the icosidodecahedra).

Its coordinates are:
Code: Select all
apacs<0, 0, 2*phi, 2*phi^2>
apacs<1, 1, phi^3, phi^3>

epacs<0, phi^2, phi^3, 2+phi>
epacs<1, phi, 2*phi^2, phi^2>

I'll upload the software models to the wiki page: rectified snub demitesseract


Also known.
Code: Select all
144   * |   4   4   0   0 |  2  2   2   4   2  0  0 |  1  1  2  2  "head" of {5}
  * 288 |   0   2   2   2 |  0  0   2   1   4  1  1 |  2  0  1  2  "arms" + "legs" of {5}
--------+-----------------+-------------------------+------------
  2   0 | 288   *   *   * |  1  1   0   1   0  0  0 |  0  1  1  1
  1   1 |   * 576   *   * |  0  0   1   1   1  0  0 |  1  0  1  1
  0   2 |   *   * 288   * |  0  0   0   0   2  1  0 |  2  0  0  1
  0   2 |   *   *   * 288 |  0  0   1   0   1  0  1 |  1  0  1  1
--------+-----------------+-------------------------+------------
  3   0 |   3   0   0   0 | 96  *   *   *   *  *  * |  0  1  1  0
  3   0 |   3   0   0   0 |  * 96   *   *   *  *  * |  0  1  0  1
  1   2 |   0   2   0   1 |  *  * 288   *   *  *  * |  1  0  1  0
  2   1 |   1   2   0   0 |  *  *   * 288   *  *  * |  0  0  1  1
  1   4 |   0   2   2   1 |  *  *   *   * 288  *  * |  1  0  0  1
  0   3 |   0   0   3   0 |  *  *   *   *   * 96  * |  2  0  0  0
  0   3 |   0   0   0   3 |  *  *   *   *   *  * 96 |  0  0  1  1
--------+-----------------+-------------------------+------------
  6  24 |   0  24  24  12 |  0  0  12   0  12  8  0 | 24  *  *  *  id
  6   0 |  12   0   0   0 |  4  4   0   0   0  0  0 |  * 24  *  *  oct (tet sym)
  3   3 |   3   6   0   3 |  1  0   3   3   0  0  1 |  *  * 96  *  oct (3-ap sym)
  3   6 |   3   6   3   3 |  0  1   0   3   3  0  1 |  *  *  * 96  teddi
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Re: Johnsonian Polytopes

Postby quickfur » Thu Mar 27, 2014 12:03 am

Klitzing wrote:
quickfur wrote:[...]
Edit 2: Hmm, apparently I forgot about the tetrahedra of the second kind in the snub 24-cell, that produces analogous truncated tetrahedra in this CRF, that sits between 4 other truncated tetrahedra. :)


There are no tetrahedra within tisadi!

Sorry I wasn't clear, I meant that the tetrahedra of the second in the snub 24-cell has its corresponding counterpart in the truncated tetrahedra in tisadi that is surrounded by other truncated tetrahedra.

Klitzing wrote:[...]
truncated sadi = tisadi (found in 2004 by Andrew Weimholt)
rectified sadi = risadi (found in 2004 by Andrew Weimholt)
Stott expanded sadi = prissi (found in 2005 by me)
[...]

Thanks for the info! Yeah, I thought these would be too obvious to have been missed for so long. :mrgreen:

What about what student91 suggested in his linked post (and the subsequent discussions), about other ico-diminished 120-cell family uniforms?
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Re: Johnsonian Polytopes

Postby quickfur » Thu Mar 27, 2014 1:15 am

So, I just constructed prissi (prismatorhombato snub 24-cell, aka "runcinated snub 24-cell"), and I'm immediately mystified by the fascinating structure of triangular cupolae that it shows. Here's a projection:

Image

These are 12 triangular cupolae that share a face with the nearest icosahedron (cyan, center). They form a fascinating formation of 6 pairs, that look like pacman waiting to gobble up the ghost. :P The "ghosts" are truncated tetrahedra. The remaining gaps are filled by triangular prisms. I'm just in awe at the interesting distribution of orientations of these triangular cupolae. They seem to reflect some kind of 4D pyritohedral symmetry -- I suppose it's just snub 24-cell symmetry. :P But nevertheless, I didn't expect this symmetry to show up in this specific way.

Very fascinating!
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Re: Johnsonian Polytopes

Postby Marek14 » Thu Mar 27, 2014 3:58 am

Hm, looking on in Stella, it seems to me that there might be a way to split the icosidodecahedra and octahedra in rectified snub 24-cell, as it's orbiform, so both of it vertex figures of this shape are fairly tame. Also, the runcinated version might have some cuts going through the icosahedra...
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Re: Johnsonian Polytopes

Postby quickfur » Thu Mar 27, 2014 4:44 am

Marek14 wrote:Hm, looking on in Stella, it seems to me that there might be a way to split the icosidodecahedra and octahedra in rectified snub 24-cell, as it's orbiform, so both of it vertex figures of this shape are fairly tame.

Are the verfs CRF by any chance? :P I'm guessing probably not, but if they are, we can probably truncate / rectify it to produce more CRFs.

I'm having trouble seeing how you could split the icosidodecahedra and octahedra, though. All of the obvious (to me) hyperplanes seem to make non-CRF cuts of some surrounding cells.

Also, the runcinated version might have some cuts going through the icosahedra...

How would you deal with the truncated tetrahedra, since they will produce bisected hexagons or other non-CRF polygons? Since the polychoron is vertex-transitive, it means any diminishing you do will modify at least one truncated tetrahedron in some non-CRF way (since there is no CRF diminishing of a truncated tetrahedron) -- unless you outright delete them all (but you'd be left with nothing :D). Or is there a way to do this that allows patching up the result with CRF pieces afterwards?
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Re: Johnsonian Polytopes

Postby Marek14 » Thu Mar 27, 2014 8:14 am

No, the verfs are not CRF -- I just noticed that there are planes that can split them, but haven't actually checked what would happen to surroundings...
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Re: Johnsonian Polytopes

Postby Klitzing » Fri Mar 28, 2014 12:07 pm

Klitzing wrote:
quickfur wrote:And of course, the rectified snub 24-cell is also CRF:

Image

It has 24 icosidodecahedra, 96 tridiminished icosahedra, 120 octahedra (divided into 24 octahedra which are surrounded only by other octahedra, and 96 octahedra that touch the icosidodecahedra).

Its coordinates are:
Code: Select all
apacs<0, 0, 2*phi, 2*phi^2>
apacs<1, 1, phi^3, phi^3>

epacs<0, phi^2, phi^3, 2+phi>
epacs<1, phi, 2*phi^2, phi^2>

I'll upload the software models to the wiki page: rectified snub demitesseract


Also known.
Code: Select all
144   * |   4   4   0   0 |  2  2   2   4   2  0  0 |  1  1  2  2  "head" of {5}
  * 288 |   0   2   2   2 |  0  0   2   1   4  1  1 |  2  0  1  2  "arms" + "legs" of {5}
--------+-----------------+-------------------------+------------
  2   0 | 288   *   *   * |  1  1   0   1   0  0  0 |  0  1  1  1
  1   1 |   * 576   *   * |  0  0   1   1   1  0  0 |  1  0  1  1
  0   2 |   *   * 288   * |  0  0   0   0   2  1  0 |  2  0  0  1
  0   2 |   *   *   * 288 |  0  0   1   0   1  0  1 |  1  0  1  1
--------+-----------------+-------------------------+------------
  3   0 |   3   0   0   0 | 96  *   *   *   *  *  * |  0  1  1  0
  3   0 |   3   0   0   0 |  * 96   *   *   *  *  * |  0  1  0  1
  1   2 |   0   2   0   1 |  *  * 288   *   *  *  * |  1  0  1  0
  2   1 |   1   2   0   0 |  *  *   * 288   *  *  * |  0  0  1  1
  1   4 |   0   2   2   1 |  *  *   *   * 288  *  * |  1  0  0  1
  0   3 |   0   0   3   0 |  *  *   *   *   * 96  * |  2  0  0  0
  0   3 |   0   0   0   3 |  *  *   *   *   *  * 96 |  0  0  1  1
--------+-----------------+-------------------------+------------
  6  24 |   0  24  24  12 |  0  0  12   0  12  8  0 | 24  *  *  *  id
  6   0 |  12   0   0   0 |  4  4   0   0   0  0  0 |  * 24  *  *  oct (tet sym)
  3   3 |   3   6   0   3 |  1  0   3   3   0  0  1 |  *  * 96  *  oct (3-ap sym)
  3   6 |   3   6   3   3 |  0  1   0   3   3  0  1 |  *  *  * 96  teddi


Just dreamed up the bilbiroing of risadi:
Take one of these tet-symmetrical octahedra, together with its 4 adjacent 3ap-octahedra and the 4 adjacent teddies.

Now attach into the dimples not ids (as in risadi) but only 6 bilbiroes. And at the still open 3ap-faces attach 4 trips, together with 3 radially emanating triangles each.

Finally close that structure with just the same fully symmetrical oct complex from above.

Here would be its incmat as well:
Code: Select all
oxFxo3xooox3ofxfo&#xt

o....3o....3o....     & | 12  *  * |  4  4  0  0  0  0 | 2 2  2  4  2 0  0  0 0 | 1 2 1 2 0  of tet-sym oct, verf = xx2xf&#x
.o...3.o...3.o...     & |  * 24  * |  0  2  2  1  1  0 | 0 0  2  1  2 1  2  1 0 | 0 1 2 1 1  of trip
..o..3..o..3..o..       |  *  * 12 |  0  0  0  2  0  2 | 0 0  0  0  4 0  0  1 1 | 0 0 2 2 0  of teddi bases, verf = xo2ox&#f
------------------------+----------+-------------------+------------------------+----------
..... x.... .....     & |  2  0  0 | 24  *  *  *  *  * | 1 1  0  1  0 0  0  0 0 | 1 1 0 1 0
oo...3oo...3oo...&#x  & |  1  1  0 |  * 48  *  *  *  * | 0 0  1  1  1 0  0  0 0 | 0 1 1 1 0
.x... ..... .....     & |  0  2  0 |  *  * 24  *  *  * | 0 0  1  0  0 1  1  0 0 | 0 1 1 0 1  at trip bases
.oo..3.oo..3.oo..&#x  & |  0  1  1 |  *  *  * 24  *  * | 0 0  0  0  2 0  0  1 0 | 0 0 2 1 0
.o.o.3.o.o.3.o.o.&#x    |  0  2  0 |  *  *  *  * 12  * | 0 0  0  0  0 0  2  1 0 | 0 0 2 0 1  trip lacings
..... ..... ..x..       |  0  0  2 |  *  *  *  *  * 12 | 0 0  0  0  2 0  0  0 1 | 0 0 1 2 0
------------------------+----------+-------------------+------------------------+----------
o....3x.... .....     & |  3  0  0 |  3  0  0  0  0  0 | 8 *  *  *  * *  *  * * | 1 1 0 0 0  oct-oct
..... x....3o....     & |  3  0  0 |  3  0  0  0  0  0 | * 8  *  *  * *  *  * * | 1 0 0 1 0  oct-teddi
ox... ..... .....&#x  & |  1  2  0 |  0  2  1  0  0  0 | * * 24  *  * *  *  * * | 0 1 1 0 0
..... xo... .....&#x  & |  2  1  0 |  1  2  0  0  0  0 | * *  * 24  * *  *  * * | 0 1 0 1 0
..... ..... ofx..&#xt & |  1  2  2 |  0  2  0  2  0  1 | * *  *  * 24 *  *  * * | 0 0 1 1 0
.x...3.o... .....     & |  0  3  0 |  0  0  3  0  0  0 | * *  *  *  * 8  *  * * | 0 1 0 0 1
.x.x. ..... .....&#x    |  0  4  0 |  0  0  2  0  2  0 | * *  *  *  * * 12  * * | 0 0 1 0 1
.ooo.3.ooo.3.ooo.&#x    |  0  2  1 |  0  0  0  2  1  0 | * *  *  *  * *  * 12 * | 0 0 2 0 0
..... ..o..3..x..       |  0  0  3 |  0  0  0  0  0  3 | * *  *  *  * *  *  * 4 | 0 0 0 2 0
------------------------+----------+-------------------+------------------------+----------
o....3x....3o....     & |  6  0  0 | 12  0  0  0  0  0 | 4 4  0  0  0 0  0  0 0 | 2 * * * *  oct (tet-sym)
ox...3xo... .....&#x  & |  3  3  0 |  3  6  3  0  0  0 | 1 0  3  3  0 1  0  0 0 | * 8 * * *  oct (as 3ap)
oxFxo ..... ofxfo&#xt   |  2  8  4 |  0  8  4  8  4  2 | 0 0  4  0  4 0  2  4 0 | * * 6 * *  bilbiro
..... xoo..3ofx..&#xt & |  3  3  3 |  3  6  0  3  0  3 | 0 1  0  3  3 0  0  0 1 | * * * 8 *  teddi
.x.x.3.o.o. .....&#x    |  0  6  0 |  0  0  6  0  3  0 | 0 0  0  0  0 2  3  0 0 | * * * * 4  trip


(I fear I might have lost track on what we already have found in all that CRFebruary. :D But suppose, that this is a new one, ain't it?)

--- rk

PS:
And furthermore, one probably might augment this structure with 6 line||bilbiro CRFs.
Question: would then the teddi-peppy adjoins become co-realmic, i.e. recombine to ikes?
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Re: Johnsonian Polytopes

Postby student91 » Fri Mar 28, 2014 1:32 pm

Klitzing wrote:[...]
Just dreamed up the bilbiroing of risadi:
[...]
(I fear I might have lost track on what we already have found in all that CRFebruary. :D But suppose, that this is a new one, ain't it?)

--- rk

PS:
And furthermore, one probably might augment this structure with 6 line||bilbiro CRFs.
Question: would then the teddi-peppy adjoins become co-realmic, i.e. recombine to ikes?

I'm afraid this structure was already found, as D9.1. This is a bilbiro-ing of o5o3x3o, with another diminishing, and because risadi is a ico-diminishing of o5o3x3o, its bilbiroing is quite analogous. Of course D9.1 has a different top section, but the interesting part is the same. This means, that when you augment it with the pseudopyramids, you indeed will get your ike back. What I think is more interesting, and what I already pointed out in this post, is that when you take D4.9.0 and delete a pentagonal pyramid, you get a pentagonal orthocupolarotunda. :] :o_o:
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Re: Johnsonian Polytopes

Postby Klitzing » Fri Mar 28, 2014 3:53 pm

student91 wrote:
Klitzing wrote:[...]
Just dreamed up the bilbiroing of risadi:
[...]
(I fear I might have lost track on what we already have found in all that CRFebruary. :D But suppose, that this is a new one, ain't it?)

--- rk

PS:
And furthermore, one probably might augment this structure with 6 line||bilbiro CRFs.
Question: would then the teddi-peppy adjoins become co-realmic, i.e. recombine to ikes?

I'm afraid this structure was already found, as D9.1. This is a bilbiro-ing of o5o3x3o, with another diminishing, and because risadi is a ico-diminishing of o5o3x3o, its bilbiroing is quite analogous. Of course D9.1 has a different top section, but the interesting part is the same. This means, that when you augment it with the pseudopyramids, you indeed will get your ike back. What I think is more interesting, and what I already pointed out in this post, is that when you take D4.9.0 and delete a pentagonal pyramid, you get a pentagonal orthocupolarotunda. :] :o_o:


First of all, there is no "D9.1" at http://hddb.teamikaria.com/wiki/Bilbirothawroid.

If you meant D4.9.1, then it definitely is different:
- There the bilbiroes are several edge lengths apart.
- Here the bilbiroes connect pairwise at the triangles of their lunes!

I'll attach a pic, in order to show the top and bottom hemisphere. Then only the 6 bilbiroes and 4 trips shall be introduced equatorially.
risadi-oct.png
risadi-oct.png (14.47 KiB) Viewed 3012 times


The cell count of my tiny figure, as already provided in the incmat, is
2 octs with full tet sym.
8 octs with trigonal pyramidal sym,
8 teddies,
6 bilbiroes, and
4 trips.
That's all!

Note that the teddies will connect pairwise (one of each hemisphere) at the 4 green triangles shown in the pic.
It rather would be related to the ursachora. As its lace tower symbol is oxFxo3xooox3ofxfo&#xt.

--- rk
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Re: Johnsonian Polytopes

Postby quickfur » Fri Mar 28, 2014 5:21 pm

Klitzing wrote:[...]
First of all, there is no "D9.1" at http://hddb.teamikaria.com/wiki/Bilbirothawroid.

FYI, the official index page is at discovery index; that's where you want to go to look up a D number. The bilbirothawroid page only contains a subset of the D numbers.

As for the CRF you described, I'll take a look into it later today, busy at work right now.
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Re: Johnsonian Polytopes

Postby Klitzing » Fri Mar 28, 2014 5:40 pm

quickfur wrote:FYI, the official index page is at discovery index; that's where you want to go to look up a D number. The bilbirothawroid page only contains a subset of the D numbers.


That's right the problem with that wiki! There are quite a lot of inter-links missing. If one does not know the URL of what one is looking for (as you obviously do), one usually cannot find that page at all! :\

--- rk
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Re: Johnsonian Polytopes

Postby quickfur » Fri Mar 28, 2014 5:46 pm

Klitzing wrote:
quickfur wrote:FYI, the official index page is at discovery index; that's where you want to go to look up a D number. The bilbirothawroid page only contains a subset of the D numbers.


That's right the problem with that wiki! There are quite a lot of inter-links missing. If one does not know the URL of what one is looking for (as you obviously do), one usually cannot find that page at all! :\

--- rk

I know... so bug Keiji to send you an invite code for the wiki so that you can edit it yourself and fix these missing links. ;)

Edit: added link to discovery index from the CRF polychora discovery project page.
Last edited by quickfur on Fri Mar 28, 2014 5:50 pm, edited 1 time in total.
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Re: Johnsonian Polytopes

Postby student91 » Fri Mar 28, 2014 5:47 pm

Klitzing wrote:
[...]

First of all, there is no "D9.1" at http://hddb.teamikaria.com/wiki/Bilbirothawroid.

If you meant D4.9.1, then it definitely is different:
[...]--- rk

ah, I see, indeed different. I guess I was a bit too fast at reading your post. :oops:
It seems to be half of the B1 of the D4.8.x-series. I wonder if the procedure of gluing two of these together will result in true bilbiro's, i.e. do the vertices of the bilbiro's lay in the same "3-space"? If it doesn't, you've certainly shown a kind of bilbiroing that might be the key to the construction of D4.11. got to go now
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Re: Johnsonian Polytopes

Postby Keiji » Fri Mar 28, 2014 6:08 pm

quickfur wrote:
Klitzing wrote:
quickfur wrote:FYI, the official index page is at discovery index; that's where you want to go to look up a D number. The bilbirothawroid page only contains a subset of the D numbers.


That's right the problem with that wiki! There are quite a lot of inter-links missing. If one does not know the URL of what one is looking for (as you obviously do), one usually cannot find that page at all! :\

--- rk

I know... so bug Keiji to send you an invite code for the wiki so that you can edit it yourself and fix these missing links. ;)


Klitzing's already on the wiki, though he hasn't made any edits: http://hddb.teamikaria.com/w/index.php? ... r=Klitzing
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Re: Johnsonian Polytopes

Postby Klitzing » Fri Mar 28, 2014 6:40 pm

student91 wrote:ah, I see, indeed different. I guess I was a bit too fast at reading your post. :oops:

No Problem.
It seems to be half of the B1 of the D4.8.x-series. I wonder if the procedure of gluing two of these together will result in true bilbiro's, i.e. do the vertices of the bilbiro's lay in the same "3-space"? If it doesn't, you've certainly shown a kind of bilbiroing that might be the key to the construction of D4.11. got to go now


Hmmm, I see. The "hemisphere" I mentioned, in fact is exactly the surroundings of the central oct of B1 of D4.8.1
Image
or of the cyan octs in
Image
of D4.11.

So you might be right, that the orientation of the bilbiroes would not be free for adequate bend (as I imposed) but rather could be pre-fixed by that partial complex already. :angry: :oops:

But then, D4.11 shows how to continue. It might even come out finally, that D4.11 would be then the bilbiroed risadi, instead!

--- rk
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