# Message #484

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] Introduction to the 4D_Cubing Group

Date: Tue, 29 Apr 2008 23:46:14 -0500

Hi David,

The computer program sounds like a cool project :) After reading this last

post, I thought I would also point you to Don’s solving code page just in

case you hadn’t seen it.

http://www.plunk.org/~hatch/MagicCubeNdSolve/

His solver is actually hooked up to the MC4D UI under "Edit->Solve (For

Real)" (we’ve wanted to do the same for MC5D, but haven’t). The reason I

mention it in the context of your email is that I’ve used it to

answer similar questions to the example you gave. By manually editing the

log files, then seeing if the resulting position is solvable, one can test

whether certain states are reachable in the 4D cube (I recently looked at

possible types of checkerboards). So again, just mentioning in case it

could help you with your current goals, but it sounds like you are already

well on your way since you are already taking down software bugs.

Btw, I have some 3^3 puzzles with the pictures on them, though I didn’t know

they were called supercubes, and I hadn’t heard of super-supercubes before.

That’s a pretty neat extension!

cya,

Roice

On Tue, Apr 29, 2008 at 9:20 PM, David Smith <djs314djs314@yahoo.com> wrote:

> Roice,

>

> Thank you very much for your reply! I really appreciate the two

> resources you kindly pointed out to me. I have actually already read

> the paper "The Rubik Tesseract", which is what got me very interested

> in the generalized problems of n^4 and n^k Rubik’s Cubes. I got

> the idea to also try supercubes and super-supercubes from the

> n^3 formulas page I referred to in my previous post. That page

> inspired me to rediscover the same formulas that Chris Hardwick did.

> An interesting thing about 4D super and super-supercubes I

> realized is that any hypercubie with more than 1 hyperfacelet can be

> twisted in the ways Keane and Kamack showed in their paper. However,

> center hypercubies, with only one hyperfacelet, can be oriented in

> 24 different positions, and they undoubtedly have certain

> restrictions related to the other hypercubies. I want to figure out

> the regular cube first though!

>

> As for the other resource you mentioned, the author of that book has

> a preprint version available for download (at

> http://web.usna.navy.mil/~wdj/books.html) which appears to be

> very complete, despite the fact that it is not the actual book.

> I have already studied it, and it was a good introduction to group

> theory and how it relates to the Rubik’s Cube.

>

> The difficult part of this task is not discovering the formula,

> but proving it is correct and not just an upper bound. That is,

> once I have ruled out the impossible permutations, I must show

> that all of the remaining permutations are actually possible.

> (Keane and Kamack actually admit they did not do this for the

> 3^5 calculation, but state that they are very confident it is

> correct.) I suppose I could use the results from that paper, the

> ones where they show using a computer program, that all of

> the remaining permutations are possible. However, this would

> be difficult to expand to higher dimensions. Therefore, I am

> writing my own computer program, whose sole purpose is to convert

> 4-dimensional Rubik’s cubes into cycle notation, that is, labeling

> every hyperfacelet with a unique number and listing, in cycles,

> where each hyperfacelet goes when each hyperface is rotated in each

> necessary direction. (I tried doing it by hand at first - not

> recommended!) I am currently sorting out bugs in the program.

> When it is working, I pan to take the output it provides and

> put that into the Computer Algebra System GAP. I would then be

> able to directly calculate the number of permutations of any

> specific 4D cube, but more importantly, I will be able to show

> how different types of hypercubies can interplay with the rest

> of the cube. (example: On the 3x3x3x3, can I actually swap

> two hyperfacelets of a 3-colored hypercubie without affecting

> the rest of the cube?) I then plan to generalize those results

> to any sized cube, perhaps by induction.

>

> Once again, thank you Roice, for your quick and detailed reply!

> I am glad I have someone else to discuss these things with.

>

> Best Regards,

>

> David

>

> Recent Activity

>

> - 1

> New Members<http://groups.yahoo.com/group/4D_Cubing/members;_ylc=X3oDMTJnNGg3NGU4BF9TAzk3MzU5NzE0BGdycElkAzEwNzE0OTI1BGdycHNwSWQDMTcwNTkyOTE0NwRzZWMDdnRsBHNsawN2bWJycwRzdGltZQMxMjA5NTIyMDA0>

>

> Visit Your Group

> <http://groups.yahoo.com/group/4D_Cubing;_ylc=X3oDMTJmYW5jOHQyBF9TAzk3MzU5NzE0BGdycElkAzEwNzE0OTI1BGdycHNwSWQDMTcwNTkyOTE0NwRzZWMDdnRsBHNsawN2Z2hwBHN0aW1lAzEyMDk1MjIwMDQ->

> Yahoo! Groups

>

> Dog Zone<http://us.ard.yahoo.com/SIG=13oljbaos/M=493064.12016263.12445670.8674578/D=groups/S=1705929147:NC/Y=YAHOO/EXP=1209529205/L=/B=iaERBkLaX.c-/J=1209522005017040/A=4836041/R=0/SIG=11o19ppl5/*http://advision.webevents.yahoo.com/dogzone/index.html>

>

> Connect w/others

>

> who love dogs.

> Yahoo! Green

>

> Get things and<http://us.ard.yahoo.com/SIG=13osk2u7t/M=493064.12016272.12948931.8674578/D=groups/S=1705929147:NC/Y=YAHOO/EXP=1209529205/L=/B=iqERBkLaX.c-/J=1209522005017040/A=5327833/R=0/SIG=1129o14gc/*http://green.yahoo.com/earth-day>

>

> get things for free.

>

> Find out how.

> Featured Y! Groups

>

> and category pages.<http://us.ard.yahoo.com/SIG=13oecc2e0/M=493064.12016306.12445698.8674578/D=groups/S=1705929147:NC/Y=YAHOO/EXP=1209529205/L=/B=i6ERBkLaX.c-/J=1209522005017040/A=4763760/R=0/SIG=11ou7otip/*http://advision.webevents.yahoo.com/bestofyahoogroups/>

>

> There is something

>

> for everyone.

> .

>

>

>