I had not heard the requirement that M be the same for all the maps. I assume the rest of the definition is that map_i(R) and map_j(R) have disjoint interiors for all i,j < n, and that union (i < n) (map_i(R)) = R. If that's the case, then we also need a scaling factor k, so map(v) = t + M(kv). If the dimension of the containing space in D, then k = (1/n) ^ (1/D) (or something like that). On Thu, Jun 21, 2018 at 5:30 AM, Joerg Arndt <arndt@jjj.de> wrote:
* Ed Pegg Jr <ed@mathpuzzle.com> [Jun 21. 2018 10:53]:
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3D rep-tiles that are not derived from 2D rep-tiles are currently quite rare.
Is this really a rep-tile? I thought for those you take a set of affine maps map_i(v) := t_i + M * v where M is a rotation (the same for all maps!) and only the translations t_i are different.
I created a few 3D fractals using 8 such maps a while ago, using either cubes, rhombic dodecahedra, or truncated octahedra. These things a lattice tilings.
Not all of them are genus 0 in the limit.
Best regards, jj
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