Number of CRF polychora

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

Re: Number of CRF polychora

Postby quickfur » Tue Mar 07, 2017 6:50 pm

Nice puzzle. Not sure I know the answer... but there's something about these constructions where you have an initial polytope P, layered on top of a phi-scaled P, and then some other vertex layers to close things up. In that sense, they are all generalizations of teddi (as triangle || phi*triangle || dual triangle).

Am I close? :D
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Re: Number of CRF polychora

Postby Klitzing » Wed Mar 08, 2017 7:32 am

quickfur wrote:Nice puzzle. Not sure I know the answer... but there's something about these constructions where you have an initial polytope P, layered on top of a phi-scaled P, and then some other vertex layers to close things up. In that sense, they are all generalizations of teddi (as triangle || phi*triangle || dual triangle).

Am I close? :D

Well teddi is obviously contained both in the 3||teddi and the tetrahedral ursachoron. But it is mibdi, which is contained in the 3-mibdi-laced-wedge. Sure, mibdi as such is just an ike diminishing as teddi is. So they surely are related somehow by the pentagon logic xfo&#x. - But beyond?

In fact those 3 have a much closer relationship than you assumed so far. ... :nod:

--- rk
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Re: Number of CRF polychora

Postby Klitzing » Thu Mar 09, 2017 9:34 pm

As there were no further trials :(  
here finally the answer comes ;) :

Code: Select all
                                      o3o           o3o                   o3o           o3o   
                                                                                              
                                                                                              
x3o                         +     x3o                   x3o     =     x3o                   x3o
                                                                                              
           f3o                               f3o                                 f3o           
    o3x           o3x                               o3x                   o3x           o3x   
                                                                                              
                                                                                              
  {3} || teddi              +       tetrahedral ursachoron      =       3-mibdi-laced-wedge   

Nice find, ain't it? 8)

--- rk
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Re: Number of CRF polychora

Postby quickfur » Thu Mar 09, 2017 10:19 pm

:o So you're saying that 3-mibdi-laced-wedge is just a stacking of tetrahedral ursachoron with {3} || teddi? Haha... and I was under the (wrong) impression that it was elementary! (I.e. can't be decomposed into smaller CRFs).

Now, I wonder if we would get something interesting if we started with an x5o3x ursachoron (don't remember what's the final name we agreed on for this), and stacked it with {6} || x5o3x? Would it be CRF? Can it be made CRF? Will it have nice symmetries?
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