ICN5D wrote:I'm currently compiling document about slices and rotations of 6D toratopes

Aw, sweet! Any illustrations? I think you mentioned Mathematica before, so probably. Would it be any better for renders, do you think? I fear that treading into 7 and 8D waters will be beyond the capacity of CalcPlot3D. Though, I'm not sure, since I haven't gone there yet. But, if it handled Triger really well, then maybe some higher derivatives of it will be just as easy. As in, those that are a trace of spheres.

I've been thinking of those 6D toratopes that are spheres along a tigroid rim, like spheric tiger ((II)(II)I), spheric torus-tiger (((II)I)(II)I), and the like. It is interesting that the trace of spheres is actually from the lowest circle-array trace, that then had a bisecting rotation of its minor diameter. It's also cool to see how it plays around with the hidden minor diameter of tigroids. It seems to be already defined by the outermost brackets, in the positions of the two markers in (II). Adding another marker, as in ((II)(II)I) has the identity of (III), a sphere. (((II)I)(II)I) ought to have some wild looking obliques, wouldn't you say?

Well, no pictures, it looks like my 5D analysis a few posts back. I'm not at 21-torus 21-tiger (the shape you've mentioned), but for example:

12. 221-tiger 1-torus (((II)(II)I)I)

3 5D slabs: minor pair of 221-tigers (((II)(II)I)), tiger torus (((II)(II))I), two 221-ditoruses stacked in medium dimension (((II)(I)I)I) and (((I)(II)I)I)

5 4D slices: minor pair of tigers (((II)(II))), vertical stack of two minor pairs of spheritoruses (((II)(I)I)) and (((I)(II)I)), two ditoruses stacked in medium dimension (((II)(I))I) and (((I)(II))I), empty slice (((II)()I)I) and ((()(II)I)I), 2x2 array of torispheres (((I)(I)I)I)

Minor pair of tigers slice can evolve into minor pair of 221-tigers slab or tiger torus slab.

Vertical stack of two minor pairs of spheritoruses slice can evolve into minor pair of 221-tigers slab and two 221-ditoruses stacked in medium dimension slab.

Two ditoruses stacked in medium dimension slice can evolve into tiger torus slab or two 221-ditoruses stacked in medium dimension slab.

Empty slice can only evolve into two 221-ditoruses stacked in medium dimension slab.

2x2 array of torispheres slice can only evolve into two 221-ditoruses stacked in medium dimension slab, but in two different ways.

6 3D cuts: vertical stack of two minor pairs of toruses (((II)(I))) and (((I)(II))), empty cut A (((II)()I)) and ((()(II)I)), 2x2 array of pairs of spheres (((I)(I)I)), empty cut B (((II)())I) and ((()(II))I), 2x2 array of toruses (((I)(I))I), empty cut C (((I)()I)I) and ((()(I)I)I)

Vertical stack of two minor pairs of toruses cut can evolve into minor pair of tigers slice, vertical stack of two minor pairs of spheritoruses slice or two ditoruses stacked in medium dimension slice.

Empty cut A can evolve into vertical stack of two minor pairs of spheritoruses slice (x2) or empty slice.

2x2 array of pairs of spheres cut can evolve into vertical stack of two minor pairs of spheritoruses slice (in two different ways) or 2x2 array of torispheres slice.

Empty cut B can evolve into two ditoruses stacked in medium dimension slice (x2) or empty slice.

2x2 array of toruses cut can evolve into two ditoruses stacked in medium dimension slice (in two different ways) or 2x2 array of torispheres slice.

Empty cut C can evolve into empty slice or 2x2 array of torispheres slice (x2).

4 rotations are animations of tiger torus.

7 new rotations: vertical stack of two minor pairs of toruses - empty cut A (((II)(x)x)), vertical stack of two minor pairs of toruses - 2x2 array of pairs of spheres (((Ix)(I)x)), empty cut A - 2x2 array of pairs of spheres (((Ix)(x)I)), 2x2 array of pairs of spheres - 2x2 array of toruses (((I)(I)x)x), 2x2 array of pairs of spheres - empty cut C (((I)(x)I)x), 2x2 array of toruses - empty cut C (((I)(x)x)I), empty cut C - alternate empty cut C (((x)(x)I)I)

3 empty rotations: empty cut A - empty cut B (((II)()x)y), empty cut A - empty cut C (((Ix)()I)x), empty cut B - empty cut C (((Ix)()x)I)

2 double rotations are animations of tiger torus.

8 new double rotations: vertical stack of two minor pairs of toruses - alternate empty cut A (((xy)(Ix)y)), vertical stack of two minor pairs of toruses - empty cut C (((Ix)(y)x)y) or (((Ix)(y)y)x), vertical stack of two minor pairs of toruses - alternate empty cut C (((xy)(I)x)y), empty cut A - alternate empty cut A (((xy)(xy)I)), empty cut A - 2x2 array of toruses (((Ix)(x)y)y) or (((Ix)(y)y)x), empty cut A - alternate empty cut C (((xy)(x)I)y), 2x2 array of pairs of spheres - empty cut B (((Ix)(x)y)y) or (((Ix)(y)x)y), empty cut B - alternate empty cut C (((xy)(x)y)I)

1 triple rotation: empty cut A - alternate empty cut B (((xy)(xy)z)z) or (((xy)(xz)z)y)