Quote:
2. Parentheses of form a1111... with b 1's evaluate to a#(b+1)
I agree with this one.
Example: (211) = 2#4, (3111) = 3#5
I just realised there's two problems here.
First, my example is wrong. (211) = 2#3 by your rule, and (3111) = 3#4. Second, in my list I have (211) = 3#2, not 2#3. However, in the wiki we have (211) = circle # sphere, which seems more correct. So I'll change the list.
Here's the 4D, 5D and 6D rotopes.
4D: 1 + 4 + 4 + 1 = 10
1111 = 1x1x1x1
211 = 2x1x1
22 = 2x2
31 = 3x1
4 = 4
(21)1 = (2#2)x1
(211) = 2#3
(22) = (2x2)#2
(31) = 3#2
((21)1) = 2#2#2
5D: 1 + 6 + 10 + 6 + 1 = 24
11111 = 1x1x1x1x1
2111 =2x1x1x1
221 = 2x2x1
311 = 3x1x1
32 = 3x2
41 = 4x1
5 = 5
(21)11 = (2#2) x1x1
(211)1 = (2#3) x1
(2111) = 2#4
(22)1 = ((2x2)#2) x1
(21)2 = (2#2)x2
(221) = (2x2)#3
(31)1 = 3#2 x1
(311) = 3#3
(32) = (3x2)#2
(41) = 4#2
((21)1)1 = 2#2#2 x1
((21)11) = (2#2)#3
((211)1) = (2#3)#2
((22)1) = ((2x2)#2)#2
((21)2) = ((2#2)x2)#2
((31)1) = ((3#2)#2)
(((21)1)1) = 2#2#2#2
6D: 1 + 10 + 23 + 23 + 8 + 1 = 66
111111
21111 , 2211 , 222 , 3111 , 321 , 33 , 411 , 42 , 51 , 6
(21)111 = 2#2 x1x1x1
(211)11 = 2#3 x1x1
(2111)1 = 2#4 x1
(21111) = 2#5
(22)11 = (2x2)#2 x1x1
(21)21 = 2#2 x2 x1
(21)(21) = (2#2)x(2#2)
(211)2 = (2#3)x2
(221)1 = (2x2)#3 x 1
(2211) = (2x2)#4
(22)2 = (2x2)#2 x 2
(222) = (2x2x2)#3
(31)11 = (3#2) x1x1
(311)1 = (3#3) x1
(3111) = 3#4
(21)3 = (2#2) x3
(31)2 = (3#2) x2
(32)1 = (3x2)#2 x1
(33) = (3x3)#2
(41)1 = 4#2 x 1
(411) = 4#3
(42) = (4x2)#2
(51) = 5#2
((21)1)11 = 2#2#2 x1x1
((21)11)1 = 2#2#3 x1
((21)111) = 2#2#4
((211)1)1 = 2#3#2 x1
((211)11) = 2#3#3
((2111)1) = 2#4#2
((22)1)1 = (2x2)#2 x1
((22)11) = (2x2)#3
((21)2)1 = ((2#2)x2)#2x1
((21)1)2 = 2#2#2 x 2
((21)21) = ((2#2)x2)#3
((21)(21)) = ((2#2)x(2#2))#2
((211)2) = ((2#3)x2)#2
((221)1) = ((2x2)#3)#2
((22)2) = (((2x2)#2) x2) #2
((31)1)1 = 3#2#2 x1
((31)11) = 3#2#3
((311)1) = 3#3#2
((21)3) = ((2#2) x 3)#2
((31)2) = ((3#2) x 2)#2
((32)1) = (3x2)#2#2
((41)1) = 4#2#2
(((21)1)1)1 = 2#2#2#2x1
(((21)1)11) = 2#2#2#3
(((21)11)1) = 2#2#3#2
(((211)1)1) = 2#3#2#2
(((22)1)1) = (2x2)#2#2#2
(((21)2)1) = ((2#2)x2)#2#2
(((21)1)2) = ((2#2#2)x2)#2
(((31)1)1) = 3#2#2#2
((((21)1)1)1) = 2#2#2#2#2