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

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?
quickfur
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Re: Number of CRF polychora

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?

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. ...

--- rk
Klitzing
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Re: Number of CRF polychora

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?

--- rk
Klitzing
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Re: Number of CRF polychora

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?
quickfur
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