Talk:Rectification (geometry)

In 3 dimensions

The top row of the rectification/dual chart is not ideal, as the rectified and dual polyhedra do not correspond exactly to the original (you need to perform some sort of rotation in your head). The other rows are much clearer in this regard. Dshin 16:51, 22 March 2006 (UTC)

I agree, ideally the images would be consistently aligned.

There's some free software that can generate images. I've used it elsewhere, but not here yet. [1]

Same issue on table at Uniform_polyhedron#Listed_by_symmetry_groups_and_vertex_arrangements

It's on my list, but not sure when I can make some better images. I'd KEEP existing nice images, and make a different set for these truncation sets for comparison.

I'm happy if you or anyone else would like to try.

Tom Ruen 09:57, 23 March 2006 (UTC)

Regarding the recent edit about a "tetratetrahedron": it seems to imply that the prefix "tetra-" is equivalent to some sort of geometric operation (?) - it would help to state this equivalence explicitly. Otherwise, I am a bit confused about where that name comes from. Dshin 20:37, 22 March 2006 (UTC)

Improved a bit? Tom Ruen 09:57, 23 March 2006 (UTC)

Yes, thank you, the names make a lot more sense to me now. I understand your statement that "polyhedron A has the faces of polyhedra B and C" to mean that A can be expressed as the intersection of appropriately scaled versions of B and C. The latter statement seemed to be a bit more precise. I modified the section to what was, in my opinion, a slightly more concise explanation of the naming schema; feel free to change it back if you wish.

I think what would really top it off is if we could modify the images so that the original polyhedra were red, the dual polyhedra were yellow, and the rectified polyhedra were red and yellow, to show which faces come from which polyhedron. Dshin 17:04, 23 March 2006 (UTC)

In 4 dimensions

The pictures here seem pretty useless, without some sort of explanation of how the 2-D representations were generated. Furthermore, the representations are of different types - the hypercube representation should parallel the others. I propose to just remove the pictures all together. Dshin 20:28, 22 March 2006 (UTC)

Agreed, images not that useful now. Tom Ruen 09:57, 23 March 2006 (UTC)

Not agreed, images help understand. Maksim-e 20:41, 29 August 2007 (UTC)

Thanks for the correction on rectified 5-cells - and yes - better pictures have been added since March 2006! Tom Ruen 00:01, 30 August 2007 (UTC)

In lower dimensions

I think it would be nice if there was a section on rectification of curves in the plane. The Wikipedia page on Arc length has a pretty picture of the rectification of a curve. Not everything has to be 3 or 4 dimensional, and a section on lower dimension rectifications might be nice. 73.14.72.177 (talk) 23:27, 25 August 2022 (UTC)

That's a completely unrelated sense of "rectification" and should not be in the same article. However, it makes sense to add a link to the other sense of "rectification", I'll do that now. --platypeanArchcow (talk) 23:33, 25 August 2022 (UTC)