Rectified {6,3,6}
Rectified {6,3,6}
Like the {3,6,3}, the geometry of the regular {6,3,6} can be quite strange because of all the infinities.
https://en.wikipedia.org/wiki/Order-6_hexagonal_tiling_honeycomb
Thank goodness for the Poincaré ball model, which allows interaction with all the elements in a finite way.
The cells of the rectified {6,3,6} are trihexagonal tilings and triangular tilings. The vertex figure is a hexagonal prism.
Like the {3,6,3}, the geometry of the regular {6,3,6} can be quite strange because of all the infinities.
https://en.wikipedia.org/wiki/Order-6_hexagonal_tiling_honeycomb
Thank goodness for the Poincaré ball model, which allows interaction with all the elements in a finite way.
The cells of the rectified {6,3,6} are trihexagonal tilings and triangular tilings. The vertex figure is a hexagonal prism.
And to think, that it has {6,4}, three non intersecting copies of it, at each vertex. Some regular groups can be set up as a mob of crossing friezes. As for poincare, i found it was terribly limited when trying to deal with the uniform 2d tilings, and we needed fancier interrupted maps to make this work.
ReplyDeleteAnd like 3,6,3, the 6,3,6 has its vertices and cell centres falling at the cell centres of a 6,3,3. The symmetries of 6,3,6 and 3,6,3 are subgroups of order 6 and 4 of 6,3,3. And likewise subgroups of order 15 and 10 of 6,3,4.