Message #804

From: Don Hatch <>
Subject: Re: [MC4D] Dimensionality Notation and Other Cubing Terminology
Date: Thu, 03 Dec 2009 18:07:07 -0500

Hi David,
Just a couple of small points in all of this…
You propose the new term "hypoface" for a sub-2-cube…
It makes sense (as does the discussion of "hypo" and "super"),
but I feel like this new term is unnecessary
since facet,ridge,peak are (fairly) standard
and clear unambiguous terms for the sub-1,2,3-cube respectively…
(and see the links at the bottom)
And, I’d definitely stay away from using "face" to mean sub-1-cube
(or anything else if possible)…
"face" is so traditionally overloaded that it will always be confusing,
and we have the very clear term "facet" which can be used instead
to mean sub-1-cube.

On Fri, Feb 06, 2009 at 09:37:06PM -0600, David Vanderschel wrote:
> <p>For 4-cubes and 5-cubes, we lack words for some of their sub-cube
> types. I think it would be helpful to have such words, especially
> since they can also be used to name cubie types for order-3 puzzles.
> For a sub-2-cube of an n-cube when n>3, I propose "hypoface". For a
> sub-(n-2)-cube of an n-cube when n>4, I propose "superedge". (Note
> that the "hypo" prefix suggests going downwards in dimensional extent,
> while "super" suggests going upwards. I would have preferred "hyper"
> to "super", but it would probably be helpful if no two names started
> with the same letter.) [Both of these suggestions are very tentative.
> I am open to alternative suggestions. (An alternative for this pair
> might be "subface" and "hyperedge"; but "subface" does not quite have
> the right ‘feel’ about it for me.)]
> <p>If you were to apply the above new names to lower dimension cubes,
> you would discover the following: For a square, a hypoface is a
> corner and a superedge is the whole square. For a 3-cube, a hypoface
> is an edge and a superedge is a face. For a 4-cube, a hypoface and a
> superedge are the same thing. (Multiple names for the same sub-level
> is a situation which already existed: E.g., on a square, face and
> edge would be the same.)