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....
It is by will alone, I set my donuts in motion
ICN5D
Pentonian
 
Posts: 1135
Joined: Mon Jul 28, 2008 4:25 am
Location: the Land of Flowers

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
Klitzing
Pentonian
 
Posts: 1637
Joined: Sun Aug 19, 2012 11:16 am
Location: Heidenheim, Germany

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
It is by will alone, I set my donuts in motion
ICN5D
Pentonian
 
Posts: 1135
Joined: Mon Jul 28, 2008 4:25 am
Location: the Land of Flowers


Return to Other Geometry

Who is online

Users browsing this forum: No registered users and 6 guests

cron