Up to now the best one imho was this:

https://tunnissen.eu/polyh/local_off.ht ... istance=15

but now I think that snub one beats all!

The penultimate is the best.

I found your model on page 41 of Wenzel Jamnitzer‘s Perspectiva Corporum Regularium: https://digital.slub-dresden.de/werkansicht/dlf/12830/41/0/ He drew a compound of it with an octahedron inside, the spikes of which are looking through the central squares of the crosses, building 4-fold pyramids on...

That‘s very nice! I never saw it before. It‘s a truncated octahedron augmented by 8 triangular cupolae (j3).
Switzerland should take a gif file of this rotating model as a flag on their website schweiz.ch.
Ulrich

You can try to augment the faces with thin prisms and then export a stl-file. It's a bit complicated and the result isn't very exact, but it should work.



Ulrich

Try in the poly-menue: add model to mirror image.

Ulrich

This is a paper model I made of a noble polyhedron senkoquartz discovered lately.
It‘s not very neat because I made it quickly with bad paper. I‘ll make a new one later.

Ulrich

Oh, sorry, you're right, it's the same. I didn't look carefully.

In the meantime I found one more pair. It is derived from an augmented dodecahedron:

I struggled with the cubic ones some time ago. Trying to reproduce Bückners 24,3 I faceted a rhombic cuboctahedron in a way Branko Grünbaum described years ago. In the preview window everything looks allright but if I hit shift ctrl F the face is splitted to coplanar triangles and I get 12 disphenoi...

Great!

I tried starting from geodesic spheres and many different bodies created with the morphing tools. Thus we get trillions of isogonal polyhedra but all isohedral facetings from these were crowns and disphenoids. All this is poking in the fog.

Ulrich

senkoquartz, your latest discoveries brought me to the following: I augmented the icosahedron with pyramids, faceted it isohedral and faceted the duals of the convex hulls of the results again. Thus I found four more noble polyhedra: https://i.postimg.cc/sBRmDPYB/Faceted-Stellated-Dual-of-Augmented-...

Ah, thanks, I got it now. The first one is really great with its pentagonal faces and I'm eager to build it in paper.

Ulrich

I was not able to reproduce this with my equipment because stella always crashes when I try to create an isohedral faceting of the small retrosnub icosicosidodecahedron's dual or its convex hull. Could you describe how you managed to do so?

Thanks
Ulrich

These are beautiful models and very pretty polyhedra/polytopes! To me it is difficult to say which one is my favorite polyhedron. It changes all day and every model I finished is my favorite one for some time. In principle, I love all uniform ones. And one of my favorite is the rhombic triacontahedr...