# Message #2732

From: schuma <mananself@gmail.com>

Subject: Re: Puzzle in Minkowski Space?

Date: Sat, 04 May 2013 05:36:59 -0000

Since I hope to construct some new things that don’t correspond to Magic Tiles, I prefer considering the solid shapes that tile the M3 space. The "cells" should be related by some translation operations and spatial rotations and Lorentz boosts. Collectively these operations are in the Poincare group:

http://en.wikipedia.org/wiki/Poincar%C3%A9_group

If we don’t do any Lorentz boost, the common cubic tiling would satisfy the constraint because we only need translations to move one cell to another. But it’s not interesting because it’s nothing new… I haven’t found any tiling that is unique in Minkowski space.

I guess maybe I should think more about cells with light-like boundaries, because light-like boundaries will stay light-like after boosts…

Nan

— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:

> But maybe one could build up some solid objects in M3 with planes, rather

> than starting with this "imaginary sphere" surface. And perhaps there

> could be new effects from that, especially say, if the object boundary

> moved into the area of the Minkowski space outside the "light cone". For

> example, what would be the meaning of a dodecahedron plopped straight

> inside M3?

>

> I hope you can come up with some new and unique puzzle concepts and puzzles!

>

> Cheers,

> Roice

>