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From: sjsmith@cs.umd.edu (Stephen Joseph Smith)
Newsgroups: rec.arts.ascii
Subject: LINE: Another hypercube (was Re: Line: Projection of a tesseract)
Date: 11 Jun 1994 21:11:43 -0500
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In article <2taa5h$h9o@gagme.wwa.com> tda10@cus.cam.ac.uk (Tim) writes:
>In article <2t8pmi$oas@gagme.wwa.com>, Bob Allison writes:
>|> [I believe this next one is a diamond.]
>|>     _________
>|>    /|\     /|\
>|>   / |  \ /  | \
>|>  /__|__/ \__|__\
>|> |\  |  | |  |  /|
>|> | \ |----|--| / |
>|> | /\-\---|---/\ |
>|> |/_____|\|_____\|
>|>  \  |  \ /  |  /
>|>   \ |  / \  | /
>|>    \|/     \|/
>|>     --------
>
>I think this is meant to be a projection of a tesseract, the 4D equivalent of
>the cube.  It consists of 8 cubes, each joined to 6 others by their faces.

It is also known as a hypercube.  It's simpler to think of as 2 cubes, joined
together point by point.


>A more common, but less symetric projection is:
>         _________
>      ,' |      //|
>    ,____|____/ / |
>   |  \  |___|,/  | 
>   |   \/____||   |
>   |   |    |||   |
>   |   |    |||___|
>   |   |____||'  /
>   |  /     \| ,'
>   |/________|/

I like Tim's better than the previous, but it doesn't show all the line
segments.  How about:

     --------
    /|\    /|\
   / | \  / | \
  /  |  \/  |  \
 /---+--/\  |   \
|\   |  \ \ |    \
| \  |  |\ \|     \
|  \ |  | \ |      \
|   \|  |  \|\      \
|    |  |   | \------\
|    |\ |   |\/      /|
|    | \|   |/|     / |
|    |  |   | |\   /  |
|    |  |\ /| | \ /   |
|    |  | |-+-+--|    | Hypercube
|    |--+-+-| |  |    | by Stephen J. J. Smith
|   / \ | |/ \|  |    | 11 June 1994
|  /   \| |   |  |    | when he should have been working
| /     \/|   |\ |    |
|/------/\|   | \|    |
 \      \ |   |  |    |
  \      \|\  |  |\   |
   \      | \ |  | \  |
    \     |\ \|  |  \ |
     \    | \ \--+---\|
      \   |  \/  |   /
       \  |  /\  |  /
        \ | /  \ | /
         \|/    \|/
          --------

- Stephen