Rectified {3,3,6} through a Fisheye Lens
Rectified {3,3,6} through a Fisheye Lens
Here's one more rectified honeycomb for this evening. The {3,3,6} has ideal tetrahedra for cells, and the vertex figure is a {3,6} tiling. So the rectified form has rectified tetrahedra (octahedra) and {3,6} tilings for cells.
This is the first I've tried the fisheye view, and I really like it. You can see much more of the honeycomb, and this makes me want to return to some of the previous renderings and try them anew.
Here's one more rectified honeycomb for this evening. The {3,3,6} has ideal tetrahedra for cells, and the vertex figure is a {3,6} tiling. So the rectified form has rectified tetrahedra (octahedra) and {3,6} tilings for cells.
This is the first I've tried the fisheye view, and I really like it. You can see much more of the honeycomb, and this makes me want to return to some of the previous renderings and try them anew.
Have you tried any of the non-wythoffian ones yet, such as my tiling of truncated cubes, 16 to a corner, or the chiral ones like the x3o:s3s5s.? This one looks interesting. It's o3x3o6o by my runes. My runes are being used to find the Johnsonian polychora, but i mainly sit on the sidelines there.
ReplyDeleteI haven't yet, though I would like to get there over time. There are so many pictures to make of the kaleidoscopic ones at the moment!
ReplyDeleteThe truncated cubes is made of crossing 3,8 and 8,4, so its a laminate tiling. The most interesting of the laminates is a tiling of the rhomboCO, and triangular prism, 16 of each at a vertex. It's a crossed frieze too, with these laminated by layers of triangular prisms. The vertex figure is the 26 vertex oxqxo8ooooo&#q.
ReplyDeleteVery nice! I see, you can see a wider field of view. Perhaps you can still make the view window limit square/rectangular?
ReplyDeleteThe resolution on the second one is about 400, which is quite good as hyperbolic projections from a point go. If you want clarity at a higher number you have to head to something different.
ReplyDeleteTom Ruen, the Pov-Ray fisheye lens renders one hemisphere of space and results in that circular cutoff. But Pov-Ray has a spherical lens too, and maybe that can be used to make the rendered image square/rectangular. I'll test and keep you posted.
ReplyDeleteI only discovered these options last night, and will be compelled to experiment more because the results are so cool :) The fisheye images seem to preserve more of the symmetry.