Message #2686

From: Roice Nelson <roice3@gmail.com>
Subject: Re: [MC4D] About me
Date: Tue, 19 Mar 2013 21:29:17 -0500

In dimension 5 and above, there are only 3 kinds of regular polytopes: the
n-simplex, the n-cube, and the n-orthoplex.

http://en.wikipedia.org/wiki/List_of_regular_polytopes#Five-dimensional_regular_polytopes_and_higher

So dimension 4 is very special, having 6 different flavors of regular
polytopes. Dimension 3 is also special, having 5. If anyone could give
insight into *why* things change for dimension 5, please do share.

Even though there is no "5D dodecahedron", there are 5D polytopes that are
at least reminiscent of the dodecahedron. They just aren’t regular. For
instance, you could make a prism based on the 120-cell, aka a {5,3,3}x{}.
I bet it’d be a horrific puzzle though!

Cheers,
Roice

On Tue, Mar 19, 2013 at 8:18 PM, Philip Strimpel <iamrubikman@yahoo.com>wrote:

>
> Hello Melinda,
> Many thanks for the kind welcome! :) What version of the 24 cell would
> you like me to solve? There are quite a few! Also, I don’t know if it is
> because my computer is two slow or not, but I can’t seem to understand how
> to twist anything besides 3^4 and 120 cell. I would really enjoy attempting
> some of the 5 and 6d puzzles. My computer is waaay too slow to even try the
> 600 cell though. :( Now THAT would be awesome to solve! Maybe even a 120
> cell pentultimate would be an idea for a future 4d puzzle! :• I am curious
> though… How come there can’t be a 5d dodecahedron? I know it would
> probably have hundreds or thousands of cells to it, but does nobody know of
> it because it would be too big to comprehend, or is it really virtually and
> physically impossible? Has anybody else thought of this? Just something to
> bring to the table…
>
> Best regards,
> Philip
>
>
> ————————————
>
> Yahoo! Groups Links
>
>
>
>