Message #315

From: David Vanderschel <DvdS@Austin.RR.com>
Subject: Re: [MC4D] Hi everyone!
Date: Mon, 14 Aug 2006 17:37:19 -0500

Welcome to the Group Ilia!

On Monday, August 14, "ilia.smilga"
<ilia.smilga@wanadoo.fr> remarked parenthetically:
>(BTW : people often call "faces" the elements of a 4D
>Rubik’s hypercube that you can twist: this is
>incorrect, because a face is 2D. The proper name for
>a "3D face" is a "cell"; a face, on a 4D Rubik’s
>hypercube, is a two-colored tessie)

In view of the fact that we are talking about
terminology for a relatively new area of endeavor, I
think use of words like "incorrect" or "proper" to
apply to such terminology is not justified. It is a
matter of convention how old words may be adapted to
apply in the new context.

IMO, when talking about the 4D analogue of the puzzle,
it is entirely appropriate to take the attitude that
the 4D analogue of a face of a 4-cube is a 3-cube and
that it is OK to call such a 4D face a "face" in this
context. I do believe that there is plenty of
opportunity for confusion, and I would urge folks to
use additional notations or comments to emphasize the
dimensionality context of what they are talking about.
For example, occasionally writing "4-face" in the
context of the 4D puzzle could be used to help
disassociate the 2D semantic reaction which seems to
cause Ilia concern with an unqualified "face".

I would say that the 4-face of the (order-3) 4-puzzle
facing in a given direction consists of the set of 27
4-stickers (3-cubes) all of which face in the given
direction.

Regards,
David V.