((ii)i) ((ii)(ii)) ((iii)ii) (iii)
4 i i i i i i
| / \ / \ / i i i
2 o i o o \|/
\ / \ / i o i i i i
1 o \ / \|/ \|/
o o o
torus tiger bi-spheric comb sphere
((IIII)I)
vv^^ ^^
((II)III) ^^
vv^^ ^^
((III)II)
The 41 cannot be turned into a 32 directly, it has to turn into a 23, then a 32. But a 32 can be turned back into a 41!
Now, with more markers comes more equals, and more radii multiply that effect. Take the 421-ditorus. The 211-ditorus is the standard minimum, allowing 3 free markers and 3 radii open for commuting. Enumerating these will give us 8 equals, the octet of the 511-ditorus:
w=1 w=3 w=5 w=5
1
/ \
1 2 1 1
/ \ /|\ / \
1 1 1 1 1 1 1 1
2 1 1 3D
3 3 1,11 1 4 4D
4 7 2,11 2 11 5D
1,21 2
5 15 3,11 4 2,111 2 11111 1 33 6D
1,31 4
2,21 4
1,22 3
6 31 4.11 2*8 3,111 4 211111 4*2 93 7D
3.21 3*8 2,211 4
2.22 1*6
ICN5D wrote:Marek, I think that's the double tiger (((II)(II))(II)), 22020-tiger. If I remember the cuts correctly, one of the 3D's is a quartet of tiger-cuts ( two vert stack torii) in vert of a square. This certainly looks like a tiger along the two ortho circles.
ICN5D wrote:Yes!! I instantly recognized it by your description. I love this forum, I've been learning so many awesome things lately. Shapes are like numbers, or matrices, with intricate combinations unique to each one. I'm going to blow everyone's mind with what I've been working on, when I get home. I found a way to enumerate ALL n-cells of every rotatope. This will allow us to complete the wiki, and even more.
ICN5D wrote:This will allow us to complete the wiki, and even more.
ICN5D wrote:But, when using expanded toratope notation, the 21210-duotorus tiger and the 21120-cylditorintigroid are both (2222), and 2222 for their open toratope version.
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