Message #2032

From: Roice Nelson <>
Subject: Klein and Gnonomic projection models
Date: Tue, 21 Feb 2012 20:57:30 -0600

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…
{3,5} Super Chop<>

…and the download<>