Necker Cube

[Ivan A Derzhanski <cbmvax!uunet!COGSCI.ED.AC.UK!iad>]

>  Date:     Thu, 12 Mar 1992 22:46:28 -0500
>  From: "Mark E. Shoulson" <shoulson@EDU.COLUMBIA.CTR>
>
>  A Necker Cube is that picture of a cube in 2D, y'know, wherein you can't
>  tell which way it is because you don't know how the lines cross?  Lessee
>  how good my ASCII is:
>
>        +-----------------+
>        |\                |\
>        | \               | \
>        |  +--------------+--+
>        |  |              |  |
>        |  |              |  |
>        |  |              |  |
>        |  |              |  |
>        +--+--------------+  |
>         \ |               \ |
>          \|                \|
>           +-----------------+
>
>  Well, you get the picture.  Those two spots where the two squares intersect
>  are ambiguous, in that you don't know which line is in front, and that
>  means you don't know which square is in front.  If you draw it so you can
>  tell, but with the disambiguation in an impossible fashion, you get the
>  famous irrational cube (q.v. various Escher prints.  _Belvedere_ is a good
>  example, as the guy in the dungeon is holding an irrational cube and
>  there's a picture of a Necker Cube on the floor with the key intersections
>  circled).

Haud a wee.  If I remember correctly, the cube in _Belvedere_ is not
an ambiguous one, because you can tell which line is which, only they
go in a way that makes it impossible for the cube to exist in real
life, like so:

        +=================+
        |\\              |\\
        ||\\             ||\\
        || +=================+
        || ||            || ||
        || ||            || ||
        || ||            || ||
        || ||            || ||
        +=================+ ||
         \\||             \\||
          \||              \||
           +=================+
Ivan