Message #1980

From: Eduard <>
Subject: Re: hemi-puzzles!
Date: Sat, 24 Dec 2011 12:55:37 -0000

Awesome, this colorful analysis of a colorful puzzle. I see I have to
return to MagicTile (after MPUlt and FlatRubik).

— In, Roice Nelson <roice3@…> wrote:
> Here’s a little more on the {3,5} 8-Color. These puzzles with
> colorings are strange, but they arise naturally from the math that
> identifies cells with each other, so I wanted to understand things a
> better.
> To do that, I made a graph of the 4 vertices, 10 edges, and 8 faces
> "rolled up". By that I mean each of these features is only shown once,
> rather than shown multiple times (with hand waving that "this face is
> identified with that one", as the MagicTile presentation requires). An
> image of my graph with default MagicTile colors is
here<<br> /1602345595/view>,
> and some observations about it are:
> - The cyan and purple cells are
> henagons<> (polygons
> with one vertex and one edge). The face twisting of these two
> nothing.
> - The blue and orange cells are degenerate triangles. They have three
> sides, but only two vertices. I initially thought they were
> digons<>,
> but they are more like a digon with a henagon subtracted out. I don’t
> if there is a special name for this polygon.
> - The red, yellow, white, and green cells are proper triangles. (By
> way, if you want to trace out the green and white triangles in the
> note that the edge that goes off the top of the screen is the same
> that comes up from the bottom.)
> - Since there are different cell types, this puzzle represents a *
> non-regular* spherical polyhedron. It was cool to realize this could
> done with MagicTile’s abstraction :)
> - Two of the vertices have 4 colors surrounding them, and two have 5
> colors surrounding them. Even so, the repeated color on a 4C vertex
> comes from different parts of a triangle, so the behavior is still
> - Since I was able to make this planar
> graph<>representation of the
> object, it was easier to see how it has the topology
> of the sphere.
> I haven’t tried to make sequences to solve it yet, but will. If anyone
> solves this puzzle, I’d love to hear about your experience with it!
> Roice
> On Fri, Dec 23, 2011 at 12:59 PM, Roice Nelson roice3@… wrote:
> > Hi all,
> >
> > I added some hemi-puzzles, all ones we haven’t seen before. The
> > hemi-dodecahedron and hemi-cube are not new, but I made them vertex
> > this time. There are also hemi-octahedron and hemi-icosahedron
> > now. All of these have the topology of the projective plane.
> >
> > I also stumbled upon a {3,5} 8-Color puzzle. The coloring is not
> > symmetrical (like the {8,3} 10-Color and some of the other
> > puzzles). It turns out to have 8 faces, 10 edges, and 4 vertices, so
the Euler
> > Characteristic <>
> > it has the topology of a sphere. I’ll try to write a little more
> > this 8C puzzle soon.
> >
> > You can download the latest by clicking
> > .
> >
> > Happy Holidays,
> > Roice
> >