5D is where everything happens?

Higher-dimensional geometry (previously "Polyshapes").

5D is where everything happens?

Postby wintersolstice » Fri Sep 16, 2011 12:04 pm

A lot of things seem to happen in 5D:

1) There's only 3 regular polytopes in 5D and above

2) there infinitly many Johnson polytopes in 5D and above (cartesian product of polygons to the Johnson solids and above)

3) the demicube ceases to be regular in 5D and is the only dimension where it is semiregular (regular faceted)

4)the unit-radius hypersphere is at maximum volume in a dmension between 5 and 6 but in whole numbers 5 is the largest size.

5) uncomfirmed: the sausage conjecture states that in 5D and above the comvex hull of any number of hypersheres is smallest when they're arranged in a line (i.e. when the convex hull is a sausage)

what else?
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Re: 5D is where everything happens?

Postby quickfur » Fri Jun 29, 2012 12:55 am

wintersolstice wrote:[...]5) uncomfirmed: the sausage conjecture states that in 5D and above the comvex hull of any number of hypersheres is smallest when they're arranged in a line (i.e. when the convex hull is a sausage)

what else?

This is an old topic, but I just noticed something funny today. The sausage conjecture is currently only proven for dimensions n≥42, even though the conjecture itself is stated for n≥5. In Douglas Adam's "Hitchhiker's Guide to the Galaxy", the answer to "life, the universe, and everything" is (humorously) computed to be 42. Upon which, the baffled protagonists embark on a quest to find out what the question was (since "life, the universe, and everything" isn't really a question per se). Now, thanks to this forum, we know what the question was: it was "What's the smallest dimension for which the Sausage Conjecture was proven to be true?" :P
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Re: 5D is where everything happens?

Postby Prashantkrishnan » Fri Dec 26, 2014 3:33 pm

What is a demicube?
People may consider as God the beings of finite higher dimensions,
though in truth, God has infinite dimensions
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Re: 5D is where everything happens?

Postby Marek14 » Fri Dec 26, 2014 9:41 pm

Prashantkrishnan wrote:What is a demicube?


If you imagine a cube as convex hull of all 2^n points with each coordinate either +1 or -1, demicube would be a convex hull of half of those points -- only those with, say, even number of +1's in their coordinates.
The difficulty with the demicube is that in 3D and 4D they are actually regular polytopes -- tetrahedron in 3D and 16-cell in 4D. However, in 5D and higher, demicube is its own special uniform shape. The 5D demicube is built from pentachora and 16-cells. Generally, n-dimensional demicube is built from (n-1)-dimensional simplexes and demicubes.
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Re: 5D is where everything happens?

Postby Ebubeonline George » Sun Apr 12, 2015 9:19 am

Please do elaborate more on this glome(4D Sphere) and 5D question below!

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Please do clarify the theory of a Glome(#4DSphere) with information also as a 3D objects, that when they are sucked into a black hole its data also will be encoded across the two-dimensional surface?


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Re: 5D is where everything happens?

Postby PWrong » Sat Apr 25, 2015 6:54 am

Wow, this spambot is actually using our own words. That's cool, I didn't know they could do that.
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Re: 5D is where everything happens?

Postby wendy » Sat Apr 25, 2015 11:33 am

Actually, it looks nothing like what the spam-bots deliver.

The spam-bots tend to cut about three lines of someone's post, and insert the link into the text, usually of the form of pass4cca or something. Usually you can search on the text and find it, although i usually can spot the original author. I look at every new post twice a day.

This one has genuine links that may have been inserted in-house, and erring on the side of innocence, i let it through. This is typical spambate. It was actually written by Richard Klitzing, but the program cut the text, added their own footer with links to their site and reposted it. Keiji killed this, so they're looking for a new way in.


J92 hexachoron

Postby xrobert » Fri Mar 06, 2015 7:54 pm
These 4 pairings then make up up a commutative diagram...

Various partial augmentations resp. diminishings also have been considered already.
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the dream we dream together is reality.
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Re: 5D is where everything happens?

Postby ICN5D » Sat Apr 25, 2015 5:08 pm

This is the most legit-looking one, yet! But, what the heck is a Nigerian eco racing team, and what would they want with fermilab? That's just silly. Oh, bots, what will you think of next??
in search of combinatoric objects of finite extent
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