Message #2033

From: schuma <>
Subject: Re: Klein and Gnonomic projection models
Date: Wed, 22 Feb 2012 07:05:40 -0000

Thanks, Roice.

I simulated the effect of the Gnomonic Megaminx using Photo Booth as follows:

For the Rubik’s cube, I can’t even do the cross in this view.


— In, Roice Nelson <roice3@…> wrote:
> If you have a moment, check out a couple new MagicTile options for
> projection models. You can now switch to the
> Klein<> model
> for hyperbolic geometry, and to the analogous
> Gnomonic<> model
> for spherical geometry. In both of these projections, geodesics appear
> straight. This means all tile edges will be straight line segments, rather
> than the circular arcs of the default projections.
> In general, slices are not geodesics and will look curved. However, since
> hemispherical slices on the sphere are geodesics, those will be
> straight. Big Chop and Super Chop puzzles are therefore quite
> interesting in the Gnomonic model, as literally everything becomes straight
> lines! I found the 2x2x2 a nice one of these to pan around.
> I went through a solve of the Rubik’s Cube using the Gnomonic projection,
> and it is strange - a bit difficult honestly, mainly since only one
> hemisphere makes it to the plane. The Megaminx may be easier since you can
> see more puzzle faces at once.
> On the hyperbolic side, the Klein model does feel like a pleasant way to
> interact with the {7,3}.
> Here are some pics…
> {7,3}<>,
> {3,7}<>,
> Megaminx<>,
> {3,5} Super Chop<>
> …and the download<>
> .
> seeya,
> Roice