Newsgroups: comp.graphics.algorithms,sci.math
Subject: Re: Cubeworld - # of shapes
From: orourke@grendel.csc.smith.edu (Joseph O'Rourke)
Date: 9 Jul 98 15:49:10 GMT

In article <35A3308D.1861@shaw.wave.ca>,
Roger Carbol  <rog@shaw.wave.ca> wrote:
>lizardbill@my-dejanews.com wrote:
> 
>> Questions:
>> Can anyone tell me exactly how many shapes are made from
>> 6 cubes?
>
>My recommendation would be to approach the 2-d problem first
>(using squares) 

Following Roger's suggestion, the 2D versions are called polyominoes,
and there is a substantial literature.  See this recent survey:

@incollection{k-p-97
, author =      "D. A. Klarner"
, title =       "Polyominoes"
, chapter =     12
, editor =      "Jacob E. Goodman and Joseph O'Rourke"
, booktitle =   "Handbook of Discrete and Computational Geometry"
, publisher =   "CRC Press LLC"
, address =     "Boca Raton, FL"
, year =        1997
, pages =       "225--242"
}