Talk:Snub order-6 square tiling

chirality ain't everything

Drawn in chiral pairs:

Nope. The symmetries of a blue triangle are symmetries of the whole. I would guess that a snub is chiral iff the fundamental domain is.

See at right the fundamental domains of the 3 4 4 system; all of my 3 4 4 renderings have the same alignment. The difference in my paired snub renderings is that one has vertices in the black triangles (one of which contains the center of the circle) and the other has vertices in the white triangles. —Tamfang (talk) 21:33, 9 November 2017 (UTC)[reply]

I'm a little confused. If you look at colors around a black triangle in each, the color order is reverse, one ccw is red-yellow-blue, other is cw red-yellow-blue, so they are mirror images. While the yellow-only square version below has reflection lines, and so isn't chiral. Tom Ruen (talk) 01:25, 10 November 2017 (UTC)[reply]

I am inclined to agree with Tamfang; it's not chiral unless you colour the faces to make it so. Which you can certainly do, but then you are not representing the full symmetry of the figure. Double sharp (talk) 03:48, 10 November 2017 (UTC)[reply]

And the only reason I made the squares red and yellow was to match the corresponding facets in my other 3 4 4 figures. —Tamfang (talk) 04:35, 18 May 2023 (UTC)[reply]