Message #2584

From: Eduard <ed.baumann@bluewin.ch>
Subject: MagicTile Solving
Date: Mon, 31 Dec 2012 14:26:40 -0000

I have startet MagicTile "MT skew {4,6|3} 30 v020".

Here too you find a remarkable property.

I remind you

Theorem of Astrelin

A 60-deg rotation of the whole puzzle "MT skew {6,4|3} 20 v200" (Roice
Nelson) around some face gives even permutation of the edges (10
6-loops) and odd permutation of centers (3 6-loops + 2 fixed points).
This is reducible to a single center swap.

The organisation of "MT skew {6,4|3} 20 v200" is

5 truncated tetrahedra TT connected by the truncation-triangles in form
of a volumecentered tetrahedron.

@

Now we have

Theorem of Baumann

A 90-deg rotation of the whole puzzle "MT skew {4,6|3} 30 v020" (Roice
Nelson) around some face gives odd permutation of the edges (15 4-loops)
and even permutation of centers (4 4-loops + 1 fixed points). The is
reducible to a single edge swap.

The organisation of "MT skew {4,6|3} 30 v020" is also interesting:

5 vertices (invisible tetrahedra) connected by 10 edges (3-prismes).
This gives 10x3 = 30 prisme-faces. See pictures.

pict 1
<http://wiki.superliminal.com/wiki/File:Pict_MT_skew_4,6-3_30_v020_a.PNG<br> > ,pict 2
<http://wiki.superliminal.com/wiki/File:Pict_MT_skew_4,6-3_30_v020_b.PNG<br> > ,pict 3
<http://wiki.superliminal.com/wiki/File:Pict_MT_skew_4,6-3_30_v020_organ<br> isation.PNG>