# Message #2729

From: schuma <mananself@gmail.com>

Subject: Re: Puzzle in Minkowski Space?

Date: Thu, 02 May 2013 22:45:07 -0000

Thanks for the attention!

OK, a 2D hyperbolic tiling lives on a 2D surface in a Minkowski 2+1 space. Here the Minkowski space is just a model that can be replaced by a disk model, say. So I think Minkowski is not essential in this application.

My question is more about, can we define 3D puzzles that fill a 3D region in a Minkowski 2+1 space?

Nan

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

> In a sense (for 2D tilings), hyperbolic tilings are the

> regular tessellations/polytopes of a Minkowski 2+1 space. E.g. one can

> think of the {7,3} living on a constant radius surface in Minkowski space,

> just as one can think of the spherical tilings living in Euclidean 3+0

> space, and the Euclidean tilings living in Euclidean 2+0 space. (Of

> course, one doesn’t have to think of all these objects being embedded in

> any of these spaces - they can be looked at just from the "intrinsic

> geometry" perspective.)

>

> I purposefully didn’t write Minkowski space*time* above by the way. One

> can still think of Minkowski 2+1 space without thinking of time. The

> "distance" between points is just calculated in a weird way, with one

> component having a negative contribution. This makes me wonder though…

> What would a {7,3} tiling look like as an animation, where that special

> component was plotted along the time dimensions? Would the regular

> heptagons even be recognizable?

>

> Roice

>