Matrixtopes defined by 3D hyperplanes?

Higher-dimensional geometry (previously "Polyshapes").

Matrixtopes defined by 3D hyperplanes?

Postby ICN5D » Thu Aug 13, 2015 4:27 am

Marek has shown me many of the matrixtopes/graphotopes that use 2D intersections to define the shape. Has an extension ever been explored that uses coordinate 3-plane (or 4-plane?) intersections to define shapes, especially when getting into 5D and 6D?

Or, is that method trivial, having no discernible benefit over the current one? If the coordinate 2-planes are second in the number sequence for binomial expansion, then perhaps it is trivial, since 2-planes will always have a lower count than 3, especially in +6D, for example,

1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1

Unless the coord 3-planes would allow for new shapes not definable with 2-planes....
in search of combinatorial objects of finite extent
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Re: Matrixtopes defined by 3D hyperplanes?

Postby Klitzing » Thu Aug 13, 2015 7:22 am

eh... what are "Matrixtopes"?
possibly you are refering to Wendy's lace cities?
--- rk
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Re: Matrixtopes defined by 3D hyperplanes?

Postby ICN5D » Fri Aug 14, 2015 12:10 am

Oh yeah, should have provided a link! This is what I'm talking about:

http://hi.gher.space/forum/viewtopic.php?p=23443#p23443
in search of combinatorial objects of finite extent
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