Message #2038

From: Eduard Baumann <baumann@mcnet.ch>
Subject: Re: [MC4D] 4D-interactive puzzles in MagicTile
Date: Sun, 04 Mar 2012 21:20:51 +0100

Awesome !!!

I like the new forms.

Question:
example { 4 4|4 }
Is this 3D or 4D. I see only 4 cells.
If 4D: are there hidden cells (as in tesseract the exterior 8th cell)?

Kind regards
Ed

—– Original Message —–
From: Roice Nelson
To: 4D_Cubing@yahoogroups.com
Sent: Sunday, March 04, 2012 5:17 PM
Subject: [MC4D] 4D-interactive puzzles in MagicTile

Recently, I learned that in addition to the regular skew polyhedra that are infinite (Melinda’s IRPs), there are regular skew polyhedra which are finite. They close back around on themselves in 4 dimensions. Here was an awesome opportunity to make MagicTile genuinely applicable to the 4D_Cubing group :D

To start, I’ve included 4D skew polyhedra associated with some duoprisms, the runcinated 5-cell, and the bitruncated 5-cell, though there are additional possibilities for the future. These should be pleasant to solve in skew mode, and I’m sure many interesting observations can be made of the shapes included so far. For instance, check out how the surface of the {4,6|3} relates to 3 intersecting spheres.

I just uploaded some pics of…
a.. {4,4|4} duoprism, aka hypercube
b.. {4,4|5} duoprism
c.. {4,4|7} duoprism
d.. {4,6|3} runcinated 5-cell
e.. {6,4|3} bitruncated 5-cell
Although the duoprisms are easily seen as having genus 1, can you figure out the genus of the other two? Not trivial to figure out by sight! I won’t give away the answer, but will say both have the same genus.

I changed the 4D viewing controls slightly from MC4D, so that the 4D camera distance could be altered with the mouse (I didn’t want to rely on a slider). Things will mostly be familiar though, and details are in the Help menu.

This feels like a great plateau, so now I’m going to take a break from MagicTile for real :)

Enjoy!
Roice