Message #2493

From: Eduard Baumann <baumann@mcnet.ch>
Subject: Re: [MC4D] New Klein Quartic puzzle by Gelatinbrain
Date: Thu, 22 Nov 2012 11:40:31 +0100

Very interesting !
Ed

—– Original Message —–
From: schuma
To: 4D_Cubing@yahoogroups.com
Sent: Thursday, November 22, 2012 8:21 AM
Subject: [MC4D] New Klein Quartic puzzle by Gelatinbrain

Hey guys,

Today Gelatinbrain added a new puzzle, called 9.1.1, in his package of puzzles. Mathematically it’s the "3C-corner-only" face-turning {7,3} F0.67:0:1 (KQ classic). Just ignore the centers and edges and you have it.

But, his visualization is quite different. Rather than fitting seven equilateral triangles around a vertex in the hyperbolic space, he fits seven triangles in an Euclidean space in a folded fashion, pretty much like the infinite regular polyhedra. But in his visualization, the whole puzzle is finite. There’s no periodic repetition or so. Gelatinbrain said: "I mapped all vertices to equilateral triangles. So there are inevitably broken edges."

The visualization is like this:

http://twistypuzzles.com/forum/download/file.php?id=33767

By dragging the puzzle to re-orient it, you can take some inside triangles out. This is not consider a twist, just a change of viewpoint. I played it for a while and I found piece-finding pretty hard. The difficulty is similar to that of infinite regular polyhedra.

Discussion on twistypuzzles:
http://twistypuzzles.com/forum/viewtopic.php?p=292407#p292407
and subsequent posts.

Download gelatinbrain:
http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/install.htm
I recommend the "install offline" option. Make sure the java runtime is available.

Overall I think this is a great addition to the family of KQ.

Nan