Date: Mon, 24 Jul 95 19:11:50 -0400
From: Robert Munafo <munafo@vgi.com >
~~~ Subject: Shallow-cut dodecahedron, and Re: Little keychain cubes

I have also noticed that the discussion on the "shallow-cut dodecahedron"
a.k.a. Hungarian "super nova" has come and gone a couple times. What I'm
talking about is a puzzle that looks like a Platonic dodecahedron (12
pentagonal faces) cut like

```     +''':'''''':'''+                +'''':'''':''''+
:   :        :   :              :    :      :    :
.:...:........:...:.            .'   .'      :    `.
:   :          :   :            :'''':'''''''':'''':
:   :            :   :          :    :          :    :
.'  .'            `.  `.        .'   .'          `.   `.
:.  :              :  .:   or   :`.  :            :  .':
:  `:                :'  :      :   `:              :'   :
+  .'`.            .'`.  +      +   .''.          .'`.   +
`.:   `.        .'   :.'        `. :   `.      .'   : .'
`.    `.    .'    .'            `.     `.  .'     .'
`.    `..'    .'                `.     ::     .'
`.  .'`.  .'                    `. .'  `. .'
`:    :'                        `.    .'
`..'                            `..'
```

and manipulated by turning a face 72 degrees around its axis of 5-fold
rotational symmetry (an operation that moves 5 edge pieces and 5 corner
pieces).

I'd like to cast the parts for one of these as well. It seems that the only
difficult part would be the 12-pointed "spindle" that holds all the center
pieces. It has to be strong, rigid and perfectly aligned. The easiest thing
would be to screw bolts into a 12-sided die (of the D&D variety) but I think
the alignment would be too poor.

```On Mon, 24 Jul 1995, Nichael Cramer wrote:
> >Does anyone know how I could get more of those little 25-cm 3x3x3 cubes that
>
> 25-Cm!?!  Damn son, you must have a helluva lot of keys!     ;-)
```

Oh, yes of course I meant to say 25 mm, not 25 cm. <-:
Of course, a 25-cm cube would be fun to have, too. I imagine it would be
about a 25x25x25, which would have about 7.3 * 10^2328 combinations (even
without considering face centers). God's Number would be well over 1000, and
even "Pons Asinorum" would be a major effort at 150 QTW. Since it's an
odd-order cube, it could be built by the simplistic "sextapole magnet"
method (each cubie has a north pole on its inward-pointing faces and a south
pole on its outward-pointing faces, except for the cubiess on the three
central planes which could be hollow steel) [-8

I'd like to get a bunch of small cubes so I can keep a bunch of cubes
in different configurations.

Probably a dumb idea, but if they're going to stay fixed, couldn't you just
paint some up?

Sort of a minimalist approach... but I have a notebook for recording
patterns. Most of what I want to do involves having a bunch of cubes in the
same pattern, then performing different transformations on each one and
comparing the results.

```- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
More software projects have gone awry for lack of calendar time than for
all other causes combined.
[Fred Brooks, _The Mythical Man-Month_, p. 14 (and again on p. 26)]
- - - - Robert P Munafo - - -  munafo@vgi.com - - - +1.617.276.8960 - - -
```