----- Original Message -----
From: "wen-shan kao" <proteon@...>
To: <polyforms@yahoogroups.com>
Sent: Monday, January 31, 2005 12:20 PM
Subject: [polyforms] Re: New Member of Polyforms Group

> --- In polyforms@yahoogroups.com, "William Rex Marshall"
> <kiwidale@a...> wrote:

[...]

> > C. J. Bouwkamp wrote a program back in 1995 to find all the ways in
> > which the 12 pentominoes would cover the surface of a cube of edge
> > length sqrt(10). (In such a tiling, the pentominoes do not have
> their
> > edges parallel to the edges of the cube.) The program found that
> there
> > were 26,358,584 distinct solutions, of which 284,402 were "nice"
> > solutions in which no pentomino folded around a corner to touch
> > itself.
> >
> Hi all:
> There are some "nice" solutions in two groups just posted on my
> puzzle note131.(first two gif: note131a.gif & note131b.gif)
> http://home.educities.edu.tw/proteon/note131.htm
> http://home.pchome.com.tw/soho/polyhex/note131.htm
> Those solutions are "distinct" or not ?
> Happy Puzzling!

Two solutions are distinct if two pentomino cubes cannot be made to coincide by
rotating or reflecting either cube. Of course, any given solution of a pentomino
cube can be cut open and unfolded into many different nets.

For example, each of the eight nets shown in your
http://home.educities.edu.tw/proteon/image/note131a.gif will fold up into the
same nice pentomino cube solution. Also, the four nets shown in
http://home.educities.edu.tw/proteon/image/note131b.gif each folds up into the
same nice pentomino cube as well. However, the nice solution that the nets in
note131a.gif will fold up into is certainly different from the nice solution
that the nets in note131b.gif will fold up into.