Message #1012

From: Andrey <>
Subject: Re: [MC4D] Magic Tiles
Date: Fri, 16 Jul 2010 04:38:18 -0000

— In, Roice Nelson <roice3@…> wrote:

> Melinda wrote:
> > I’m not sure what you mean by "finite factor-lattices of dodecahedral
> > honeycomb". That sounds to me like simply the 120-cell.
> I was wondering what Andrey meant by this as well. I thought maybe he was
> asking about a hyperbolic dodecahedral
> honeycomb<>,
> and whether you could cover the entire infinite space by coloring the cells
> in a repeating manner using a finite number of colors. I haven’t seen any
> info on whether this is possible (and what the corresponding topologies
> might be), but I’d love to be pointed to it.
Yes, you are right. Question is about the periodic (in some sense) paintings of dodecahedral honeycomb. I can easily imagine one (in 2 colors - we have 4 dodecahedra meeting at each edge so checkerboard painting is possible) but is there something more?
Another question is about splitting of dodecahedron in such puzzle, but we always have "non-geometric" variant based on megaminx splitting: when you twist a cell you catch 3 stickers from the edge of the cell that is connected by edge to yours and one corner sticker from the face that is connected by vertex, and don’t create extra sub-edge and sub-corner 1C stickers. Animation will be with intersections of stickers, but dodecahedra are round enough :)