# Message #1520

From: Andrey <andreyastrelin@yahoo.com>

Subject: Re: new hemi-cube and hemi-dodecahedron puzzles

Date: Mon, 07 Mar 2011 21:09:48 -0000

Nan,

I haven’t meet single 120-deg twisted corner in my two twists, but now, when you mentioned it, I agree - it’s really nice (but simple).

I think that Klein bottle-formed puzzles of type {6,3} are possible. It’s a matter of coloring, and if you take something like

.a.b.c.a.b.c

d.e.f.d.e.f.

.g.h.i.g.h.i

c.b.a.c.b.a.

.f.e.d.f.e.d

i.h.g.i.h.g.

.a.b.c.a.b.c

you will get what you want (but colors are not equivalent here).

I don’t see problems in 4-length - but it looks like 5-length puzzle with some missing pieces (like cell centers). And some couples of stickers are always glued together. But I never tried "kilominx", so I don’t know what I should expect.

If you twist opposite sides in same direction (relative to sphee surface), you’ll get orientable puzzle. I don’t know, if there are sphere paintings that are invariant to this transformation (i.e. order of adjacent colors of all intances of one face is the same). There is 5-color painting if icosahedron (all faces of outscribed tetrahedra have the same color), but I’m not sure that it will work.

Andrey