# Message #2037

From: Roice Nelson <roice3@gmail.com>

Subject: 4D-interactive puzzles in MagicTile

Date: Sun, 04 Mar 2012 10:17:07 -0600

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 <http://en.wikipedia.org/wiki/Regular_skew_polyhedron> 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<http://groups.yahoo.com/group/4D_Cubing/photos/album/597055459/pic/list>of…

- {4,4|4} duoprism, aka hypercube
- {4,4|5} duoprism
- {4,4|7} duoprism
- {4,6|3} runcinated 5-cell
- {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! <http://www.gravitation3d.com/magictile/downloads/MagicTile_v2.zip>

Roice