Impressively beautiful. Masterful craftsmanship, as always

Hi

I created my own web-page about Crossohedra. Then I have all the freedom, e.g. use "Crossohedra" instead of Sharpohedron. The page is here:
https://tunnissen.eu/polyh/crossohedra/list.html
And it is far from complete and needs a lot of work still.
To this page I added a few Crossohedra with ...

Added
https://tunnissen.eu/polyh/local_off.ht ... istance=23
https://tunnissen.eu/polyh/local_off.ht ... istance=27
to the list below

Updated the list below:
Renamed
crosso-S4xI_o2o4.off to crosso-S4xI-o2_and_o4.off

Added:
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off/crosso/crosso-S4xI-o2_and_o4-faceted.off&distance=45&stencil=on
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off/crosso/crosso-S4xI-o4_to_o3 ...

In some cases where the crosses are on the 2-fold axes it could be a good idea to extend the crosses to obtain regular faces. E.g.
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off/crosso/elongated_crosso-S4A4-o2.off&distance=25
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off ...

Updated the list below
Added one by Ulrich:
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off/crosso/Faceted_Augmented_Trunc_Cubocta_2.off&distance=40&stencil=on
Also did some renaming and added this one
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off/crosso/crosso-S4xI-o4_to_o3 ...

Updated the list below

I updated the list below. Almost all names were updated. I will try to keep that list up to date. the links from the other posts might become broken later.

Added one with prism symmetry to the list below:
https://tunnissen.eu/polyh/local_off.ht ... istance=20 (by Don Romano)

Ulrich wrote: Mon Mar 15, 2021 7:37 am Up to now the best one imho was this:
https://tunnissen.eu/polyh/local_off.ht ... istance=15

Yes, that one I like too. I built a model of the first one, but that one is going to be the next one. The snub, I didn't like so much, though.

Added a snub to the list below.
https://tunnissen.eu/polyh/local_off.ht ... istance=25

The penultimate is the best.


Which one is that?

I updated the list from before with
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off/crosso/crosso-s4xi_o2o4.off&distance=42 (by Don Romano)
https://tunnissen.eu/polyh/local_off.html?off_file=etc/off/crosso/crosso-o2_3.off&distance=35

I found some more variations on this theme. So are super simple and some can be found in Brückner, some are quite neat, though they are probably rediscoveries, but that doesn't spoil the fun.

The following models were found by Don Romano, Ulrich Mikloweit and me (last updated 2021-03-17 ...

Good found, thanks Ulrich, also from my friend Don! I was quite convinced this would be a rediscovery, since it was such a simple model. Apparently it was known at least in 1568. I think I will build a model of it in the Swiss colours. And I might look into more of these "positive" models.

Cheers ...

Yes, that is another way of looking at it!

It seems that in his book from 1900 Brückner did come a"cross" some polyhedra with the cross (as pointed out by my friend). See for instance on the right side of plate 8: row 1, #2 and row 3, #2. The former can easily be transformed by moving the crosses ...