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Mail-from: From cube-lovers-request@life.ai.mit.edu Sun Mar 29 19:35:16 1998
Date: Sun, 29 Mar 1998 19:35:43 -0400 (EDT)
From: Jerry Bryan
Subject: Re: partial isoglyphs
In-Reply-To: <199708210441.AAA22489@life.ai.mit.edu>
To: Cube-Lovers
Message-Id:
On Thu, 21 Aug 1997, michael reid wrote:
> dan recently introduced the concept of "partial isoglyphs", in which
> some faces are solid, and the others are glyphs of the same pattern.
> i looked into this a little and didn't find much. only the case
> of two opposite solid faces seems to have many possible glyph types,
> although some of these possible types may have many solutions.
>
> here's what i found
Note that all the glyph types which Mike lists (01, 02, 0D, 04, and 03 in
Dan's taxonomy) fix the corners. Thus, his note below points out that in
order to have anything other than two solid faces opposite to each other,
you must fix the corners.
The correspondence between Dan's taxonomy and my charts is 01=BF, 02=AF,
03=A7, 04=A5, and 0D=BD. As I said earlier, the identfication numbers on
my charts are not a taxonomy. Rather, they provide a unique
identification for each of the 2^8 glyphs.
>
> 6 solid faces: start
> 5 solid faces: no possibilities
> 4 solid faces:
> other two faces opposite: types 02, 0D and 04 are possible
All three possibilities do occur in my chart.
> other two faces adjacent: type 0D is possible
This possibility does occur in my chart.
> 3 solid faces:
> mutually adjacent: type 02 is possible
This possibility does occur in my chart.
> not mutually adjacent: types 01 and 0D are possible
Both possibilities do occur in my chart.
> 2 solid faces:
> adjacent: types 01, 02, 0D and 03 are possible
All four possibilities do occur in my chart.
> opposite: many possible types
Indeed!
> 1 solid face: types 01, 02 and 0D are possible
>
All three possibilities do occur in my chart. In addition, I found three
partial isoglyphs of type 03 with one solid face.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us
Pellissippi State (423) 539-7198
10915 Hardin Valley Road (423) 694-6435 (fax)
P.O. Box 22990
Knoxville, TN 37933-0990