Keiji wrote:quickfur wrote:Hmm. This is probably not hard to construct, because I already listed the vertices of the BXD on my website, so all you have to do, is to go through the 600-cell's vertices and delete all of the BXD vertices. Since the BXD contains 3 copies of the 24-cell, this should leave the vertices of 2 24-cells, which is what you want. Then you just send the result to makepoly, and off you go.
Okay, I worked out the vertices, and here's the links to the .def and .off files.
Sadly it's not* CRF, but guess what it is?
That cell right there is the cell that shows up in the dual of BXD. The element counts are BXD's element counts reversed, so I'm quite inclined to suggest this polytope is indeed the dual of BXD!
edit: *unless it actually is CRF and the cells are skew polyhedra, somehow? How do you verify all edge lengths equal with polyview?
calc edgelen
# or "calc elen" for short
Keiji wrote:[...]
That cell right there is the cell that shows up in the dual of BXD. The element counts are BXD's element counts reversed, so I'm quite inclined to suggest this polytope is indeed the dual of BXD!
[...]
quickfur wrote:Does the dual of BXD also have 9 cells around each vertex?
quickfur wrote:Keiji wrote:quickfur wrote:Hmm. This is probably not hard to construct, because I already listed the vertices of the BXD on my website, so all you have to do, is to go through the 600-cell's vertices and delete all of the BXD vertices. Since the BXD contains 3 copies of the 24-cell, this should leave the vertices of 2 24-cells, which is what you want. Then you just send the result to makepoly, and off you go.
Okay, I worked out the vertices, and here's the links to the .def and .off files.
Sadly it's not* CRF, but guess what it is?
That cell right there is the cell that shows up in the dual of BXD. The element counts are BXD's element counts reversed, so I'm quite inclined to suggest this polytope is indeed the dual of BXD!
Whoa. That's insane, if it's actually the dual of BXD!! It would be the first example of a polytope (that I know of, anyway), where the dual is derived by deleting 1/3 the vertices of the original!
Klitzing wrote:Well, that was already well-known.
And moreover, this is far more general, valide for the whole family:
ike = x3o5o --> ike - 3gon = teddi --> ike - 2x 3gon = teddi dual --> ike - 3x 3gon = ike dual = doe
ex = x3o3o5o --> ex - ico = sadi --> ike - 2x ico = bidex --> ex - 3x ico = bidex dual --> ex - 4x ico = sadi dual --> ex - 5x ico = ex dual = hi
Keiji wrote:[...]
Looks like Marek has confirmed it anyway. My first thought was to load the .off file in Stella for myself, but you need to buy the full version to load .off files
dissect polytope.def dual | makepoly dual_polytope - dual.def
[...]
Also, is there a way to "extract" a cell in polyview to its own .def file, so that it can be rendered independently as a 3D figure?
load polytope.def
select ... [some cell specification here]
list vertices in selection
polyview -qes getcell.pvs | sed -e's/.*: //' | makepoly -fperm single_cell - single_cell.def
load single_cell.def
parallel
translate to center
povfile single_cell.pov
render
quickfur wrote:Keiji wrote:[...]
Also, is there a way to "extract" a cell in polyview to its own .def file, so that it can be rendered independently as a 3D figure?
[...]
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