## Min-frame rotatopes

Discussion of shapes with curves and holes in various dimensions.

### Min-frame rotatopes

It turns out my conjecture about these was wrong. I expected that you could get the n'th homology group of a rotatope just by counting the n-spheres, except with an extra Z at the beginning and end. I've just found a few exceptions.

H222 = 1,3,0,1 as expected.
H322 = 1,2,3,0,1 where we expected 1,2,1,0,1
H332 = 1,1,2,4,0,1 where we expect 1,1,2,0,0,1

I can't see any connection yet. I'll have to do a few more.

PWrong
Pentonian

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### Re: Min-frame rotatopes

Ok I've invented a new notation for homology groups. Usually we would say
Z, 5Z, 0, 0, 0, Z.
This is annoying because you have to count all the zeroes. Instead we can write
h0 + 5h1 + h5.

Now I've also found formulae for some more rotatopes.
I write Tn for the Cartesian product of n circles e.g. T^2 = 22.

H T^n = h_0 + n h_1 + h_n
H 3T^n = h_0 + n h_1 + h_2 + 2h_n + h_n+2

I've also got 33T^n and I'm working on 4T^n.
All of these only work for n>1.

PWrong
Pentonian

Posts: 1599
Joined: Fri Jan 30, 2004 8:21 am
Location: Perth, Australia

### Re: Min-frame rotatopes

Everything in this thread is wrong now .

PWrong
Pentonian

Posts: 1599
Joined: Fri Jan 30, 2004 8:21 am
Location: Perth, Australia

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