I <3 Cuboids!

Joshua Bell · **Posted:** Fri Jun 24, 2011 9:31 pm

Cuboids by inexorabletash, on Flickr (visit for roll-over identification)

My cuboid collection:

1x1x1 Silly Custom
1x1x2 Silly Custom
1x1x3 Silly Custom
1x2x2 Minimis by VeryWetPaint (Shapeways)
1x2x3 Custom
1x3x3 Okamoto's Floppy Cube (Gentosha)
2x2x2 Rubik's Pocket Cube
2x2x3 Okamoto's Slim Tower (Gentosha)
2x2x4 Rubik's Tower (Megahouse)
2x3x3 QJ
2x3x4 Garrett Ong (Shapeways)
3x3x3 Rubik's Cube
3x3x4 Cube4You
3x3x5 Custom (from WitEden Super 3x3x3)
3x3x6 WitEden
3x4x4 Garrett Ong (Shapeways)
3x4x5 TomZ (Shapeways) - newest addition!
4x4x4 Rubik's Revenge / Master Cube
4x4x5 Ayi's Toy
5x5x5 Rubik's Professor Cube
6x6x6 V-Cube 6
7x7x7 V-Cube 7

Hopefully soon to be joined by:
2x4x4 by Olz (on order from Shapeways)
4x4x6 being designed by TomZ
4x5x5 being refined by Ayi
2x3x5 which I'm planning to hand-craft out of a QJ 2x3x3 - will post plans so folks can follow along

On my "maybe" list:
1x3x4 by Styrene/Olz (still making these?)
3x3x9 WitEden (despite not being fully functional, it's attractive)

Further NxNxNs and LxMxNs are tempting, but (despite great respect for Oskar, Olz, Traiphum and company) I think I'm going to pass on acquiring more members of the 1x2xN "Twist Family", the 1xNxN "Floppy Family", the 2x2xN "Tower Family", the 2xNxN "Domino Family", the 3x3xN "3x3 Family" and whatever we might call the 3xNxN family.

(I also look forward to digging my 2x2x3 and 2x3x3 Tony Fisher-style transforms out of storage this summer. They've been sadly neglected since the mass produced ones appeared.)

elijah · **Joined:** Sat Mar 29, 2008 12:55 am **Location:** WA, USA

*drools*

Me want!
I just hope someday that my cuboid family looks as full as yours!
Although, I do own one cuboid that you don't have. :wink:

Andreas Nortmann · **Posted:** Sat Jun 25, 2011 1:13 am

Quite impressive.
That reminds me the get the 2x4x4 too.
It is the only one missing in the <=4-section.

traiphum · **Posted:** Sat Jun 25, 2011 3:05 am

I love cuboid, nice picture.
I also have a cuboid is in processing :wink:

Luke · **Posted:** Sat Jun 25, 2011 11:31 am

Beautiful cuboid collection! It's really good. I hope one day I can have a cuboid collection like this.

Rouricht · **Joined:** Sat Oct 16, 2010 2:14 pm **Location:** Germany

traiphum wrote:

I love cuboid, nice picture.
I also have a cuboid is in processing :wink:

4x4x6 ?

DDD

pirsquared · **Posted:** Sat Jun 25, 2011 1:05 pm

That is quite an impressive picture!

-Eitan

Sigurd · **Posted:** Sat Jun 25, 2011 4:05 pm

I love that picture! You have one I would very much like to own! the 4x4x3! I am also waiting for the 4x4x6 to be designed! I really cant wait for it!

There might be another really interesting one coming in a shapeways shop soon..

yummyyummypbj · **Joined:** Mon Nov 16, 2009 10:50 am

Don't pity me for getting this wrong, but isn't the v-cube 7 not a cuboid?

Joshua Bell · **Posted:** Sat Jun 25, 2011 11:36 pm

elijah wrote:

Although, I do own one cuboid that you don't have. :wink:

The 1x4x4 Floppy Revenge? If so, did you get it working?

Sigurd wrote:

There might be another really interesting one coming in a shapeways shop soon..

Tease!

yummyyummypbj wrote:

isn't the v-cube 7 not a cuboid?

I'm going with a liberal definition of cuboid here. Pillowed (like the V-Cube 7), Olzed (I don't have any yet), or non-proportional (like the WitEden 3x3x6 and - marginally - the V-Cube 6). Even the Okamoto's floppy deformation diverges slightly from the "purity" of the cuboid concept. I just don't have the more extreme examples.

What I'm saying is: I wouldn't kick your 1x9x9 out of bed.

elijah · **Joined:** Sat Mar 29, 2008 12:55 am **Location:** WA, USA

naw, not the 4x4x1, that one wasn't fit for casting. I did get the 5x5x2 working though, and still have it, even though it doesn't turn the best. I still need to get back to redoing those molds and recasting a better tighter version of that. I just hope my silicone rubber or smoothcast hasn't gone bad after about a year...

leopulga · **Joined:** Sun Mar 15, 2009 12:00 am

They are all fully functional right?

Konrad · **Posted:** Mon Jun 27, 2011 1:39 pm

My list is quite similar

:

1x2x2 Minimis by VeryWetPaint (Shapeways)
1x2x3 Custom by TomZ
1x3x3 Okamoto's Floppy Cube (Gentosha) + Okamoto's Scramble Cube
2x2x2 Rubik's Pocket Cube (+ Eastsheen, V-Cube variants)
2x2x3 Okamoto's Slim Tower (Gentosha) + Super 2x2x3
2x2x4 Rubik's Tower (Megahouse) signed by Hidetoshi san
2x3x3 QJ + several Crazy
2x3x4 Garrett Ong (Shapeways) [color=#4000FF]+ Traiphum's handmade3x3x3 Rubik's Cube[/color]
3x3x4 Cube4You + Witeden Super 3x3x4
3x3x5 Cube4You + Witeden Super 3x3x5
3x3x6 WitEden
+ 3x3x7 Cube4You
3x4x4 Garrett Ong (Shapeways) this one I'm missing

3x4x5 TomZ (Shapeways) - newest mine is a prototype but close to the last edition
4x4x4 Rubik's Revenge + Eatsheen
4x4x5 Ayi's Toy + Garrett's Shapeways
5x5x5 Rubik's Professor+ V-Cube + Eastsheen
6x6x6 V-Cube 6
7x7x7 V-Cube 7

Ender Delphiki · **Joined:** Wed Jan 28, 2009 7:55 pm **Location:** Montana

Isn't the 5x5x5 the Rubik's Professor?

Joshua Bell · **Posted:** Mon Jun 27, 2011 8:29 pm

Rentlix wrote:

Isn't the 5x5x5 the Rubik's Professor?

Oops! Quite right - fixed!

Ender Delphiki · **Joined:** Wed Jan 28, 2009 7:55 pm **Location:** Montana

I saw it in your post and thought 'it's just a typo' but then I asked because Konrad said it as well.

traiphum · **Posted:** Mon Jun 27, 2011 10:38 pm

Rouricht wrote:

traiphum wrote:

........ in processing

4x4x6 ?

Over is 6

addition: 4x4x6=96
over is 6 is 96-6=90
90=3x3x10

Konrad · **Posted:** Tue Jun 28, 2011 2:10 am

Rentlix wrote:

I saw it in your post and thought 'it's just a typo' but then I asked because Konrad said it as well.

I had just quoted it and have not recognized the error. Have fixed it as well.

Superbud9123 · **Joined:** Thu Dec 30, 2010 12:32 am

Woah! That is a lot of cuboids! I especially like the 2x3x4. I hope that one day it will be mass-produced. :'(

Joshua Bell · **Posted:** Thu Jul 21, 2011 9:40 pm

MOAR CUBOIDS!!!!!!!!!!

Cuboids (Updated) by inexorabletash, on Flickr

As above, but adding:

* 2x4x4 by Ola Jansson http://www.shapeways.com/model/206839/ - had this for a while but (1) accidentally ordered the non-mini 2x2x2 for the kernel, so had to re-order, and (2) ran out of stickers and had to wait for more to arrive. The kernel needs to be cut down severely - there's very little of the outer shell left when you're done! But the puzzle turns very nicely. I'm using vinyl 3x3x3 stickers and just letting them flex over the olzed cuts, floppy-style.

* 2x3x5 by me! viewtopic.php?f=9&t=21510

elijah · **Joined:** Sat Mar 29, 2008 12:55 am **Location:** WA, USA

you have 18/29 non trivial cuboids with max dimensions of 5.
Very good job.

I love the 2x3x5! :mrgreen:

edit: the only ones you are missing are the 4x4x1, 5x5x1, 5x5x2, 5x5x3, 5x5x4, 2x2x5, 2x4x1, 2x5x1, 3x4x1, 3x5x1, and the 5x4x2, I believe...

Andreas Nortmann · **Posted:** Sat Jul 23, 2011 3:15 am

The 1x3x3 need to be restickered.

GoombaGeek · **Posted:** Sat Jul 23, 2011 5:28 pm

Are you getting a 3x3x7, or do you only like proportional cuboids?

Joshua Bell · **Posted:** Sat Jul 23, 2011 7:35 pm

elijah wrote:

you have 18/29 non trivial cuboids with max dimensions of 5.

edit: the only ones you are missing are the 4x4x1, 5x5x1, 5x5x2, 5x5x3, 5x5x4, 2x2x5, 2x4x1, 2x5x1, 3x4x1, 3x5x1, and the 5x4x2, I believe...

Hrmmmm, I count 18 out of 30:

122 yep
123 yep
124 nope
125 nope
133 yep
134 nope
135 nope
144 nope
145 nope
155 nope
222 yep
223 yep
224 yep
225 nope
233 yep
234 yep
235 yep
244 yep
245 nope
255 nope
333 yep
334 yep
335 yep
344 yep
345 yep
355 nope
444 yep
445 yep
455 nope (will get one from Ayi soon, I hope!)
555 yep

Andreas Nortmann wrote:

The 1x3x3 need to be restickered.

As does the 2x2x3 technically, I just caught it at a good angle. And you'll note I'm only showing the white/red/green corners...

I need to resticker the 1x2x3 as well, since the standard color scheme for the irregulars has the largest side white, medium side green, smallest side red.

GoombaGeek wrote:

Are you getting a 3x3x7, or do you only like proportional cuboids?

Proportional, but I will probably break down and get one once the 3x3x9 is out.

Jhahoua · **Joined:** Fri Jul 08, 2011 5:58 pm **Location:** Earth,

3x3x9? I have not heard about this do you have a link?

Thank you for the pics of your cuboids.

eye2eye · **Posted:** Sat Jul 23, 2011 8:06 pm

elijah wrote:

you have 18/29 non trivial cuboids with max dimensions of 5.
Very good job.

I love the 2x3x5! :mrgreen:

edit: the only ones you are missing are the 4x4x1, 5x5x1, 5x5x2, 5x5x3, 5x5x4, 2x2x5, 2x4x1, 2x5x1, 3x4x1, 3x5x1, and the 5x4x2, I believe...

You didn’t list that he doesn’t have a 3x3x5 that would bump it to 30

Joshua Bell · **Posted:** Sat Jul 23, 2011 10:28 pm

Jhahoua wrote:

3x3x9? I have not heard about this do you have a link?

EDIT: see correct link in next comment

eye2eye wrote:

You didn’t list that he doesn’t have a 3x3x5 that would bump it to 30

I do! He missed the 1x4x5.

eye2eye · **Posted:** Sat Jul 23, 2011 10:51 pm

Oh my mistake you don’t have a 3x5x5. I thought that was a pretty basic one to be missing.
Also I think you mean this link http://www.twistypuzzles.com/forum/viewtopic.php?f=15&t=21009&hilit=3x3x9 that one sent me to a tuttminx thread

Joshua Bell · **Posted:** Sat Jul 23, 2011 10:59 pm

Oops, yes, must have copied the URL incorrectly.

elijah · **Joined:** Sat Mar 29, 2008 12:55 am **Location:** WA, USA

ah, I new 29 was a weird number. I was like, "I swear there has to be another one... 30 is a better number..."
anyway, thank you for correcting me, yes, so, you are missing 12.

Joshua Bell · **Posted:** Mon Aug 08, 2011 3:29 am

elijah wrote:

naw, not the 4x4x1, that one wasn't fit for casting. I did get the 5x5x2 working though, and still have it, even though it doesn't turn the best. I still need to get back to redoing those molds and recasting a better tighter version of that. I just hope my silicone rubber or smoothcast hasn't gone bad after about a year...

If you do breakout the casting materials, please sign me up for one of your 5x5x2s!

PotatoSpades22095 · **Joined:** Sun Sep 28, 2008 9:56 pm

Can you make a video showing all of them, and showing that each is fully functional?

Jhahoua · **Joined:** Fri Jul 08, 2011 5:58 pm **Location:** Earth,

@Joshua Bell You should get the 3x3x9 they are very good.

I got mine a few das ago and it is a lot of fun.

Joshua Bell · **Posted:** Mon Oct 10, 2011 11:34 pm

Jhahoua wrote:

You should get the 3x3x9 they are very good.

Funny you should mention that...

Cuboids! by inexorabletash, on Flickr

New additions:

This brings my list to:

1x1x1 Silly Custom
1x1x2 Silly Custom
1x1x3 Silly Custom
1x2x2 Minimis by VeryWetPaint (Shapeways)
1x2x3 Custom
1x3x3 Okamoto's Floppy Cube (Gentosha)
1x3x4 by Steryne
2x2x2 Rubik's Pocket Cube
2x2x3 Okamoto's Slim Tower (Gentosha)
2x2x4 Rubik's Tower (Megahouse)
2x3x3 QJ
2x3x4 Garrett Ong (Shapeways)
2x3x5 Custom (from QJ 2x3x3)
2x4x4 by Olz
3x3x3 Rubik's Cube
3x3x4 Cube4You
3x3x5 Custom (from WitEden Super 3x3x3)
3x3x6 WitEden
3x3x9 WitEden
3x4x4 Garrett Ong (Shapeways)
3x4x5 TomZ (Shapeways) - newest addition!
4x4x4 Rubik's Revenge / Master Cube
4x4x5 Ayi's Toy
4x4x6 by TomZ
5x5x5 Rubik's Professor Cube
6x6x6 V-Cube 6
7x7x7 V-Cube 7

On the "hopefully soon" list:

On the "maybe someday" wish list:

True Cuboid: 2x3x7 e.g. Clay & Eva's
True Cuboid: 5x5x6 e.g. Steryne's WIP
True Cuboid: 5x5x7 e.g. Olz/Incredible
Pillow/Olzed: 1x4x4 by Olz
Pillow/Olzed: 2x5x5 by Olz
Olzed: 1x3x5 by Door/Incredible
Olzed: 3x4x6 by Door/Incredible
Olzed: 5x7x7 by Olz/Incredible

PotatoSpades22095 wrote:

Can you make a video showing all of them, and showing that each is fully functional?

Then you'd see my messy house.

How about this instead:

Cuboids - Checkerboarded by inexorabletash, on Flickr

I forgot to scramble the 1x1xNs. Sorry - I promise they're fully functional. Even the 1x1x1.

Joshua Bell · **Posted:** Tue Oct 11, 2011 11:19 pm

Just a little cuboid philosophy.

Obviously, Rob's Puzzle Page is the canonical source of information, and organizes the cuboids in the convenient L<=N<=M order. But it's also convenient to group them into families. Sorry for the lack of links.

== NxNxM ==

Arranged by N...
2x2x1 ... 2x2x9, 2x2x23
3x3x1 ... 3x3x10
4x4x1 ... 4x4x6
5x5x1 ... 5x5x7
6x6x6 (Did clauswe ever finish his 6x6x4?)
7x7x5, 7x7x7
8x8x8
9x9x1, 9x9x9
11x11x11
12x12x12
17x17x17

You can also slice arrange these by the M rather than the N of course, giving you the 1xNxN family, the 2xNxN family, etc.

== Nx(N+1)x(N+2) ==
1x2x3
2x3x4
3x4x5
4x5x6 - Not yet made ???

== Nx(N+1)x(N+2) ==
1x2x4
2x3x5
3x4x6
4x5x7 - Not yet made ???

== Nx(N+1)x(N+3) ==
1x2x5
2x3x6 - Not yet made ???
3x4x7 - Not yet made ???

== Nx(N+2)x(N+3) ==
1x3x4
2x4x5 (announced today!)
3x5x6 - Not yet made ???

== Nx(N+2)x(N+4) ==
1x3x5
2x4x6 - Not yet made ???
3x5x7 - Not yet made (fully functional)

Obviously this keeps going as you increase the disparity between the dimensions, e.g. the 1x2xN series, the 2x3x7, and so forth. The puzzles take on extreme shapes - sticks and slabs.

Joshua Bell · **Posted:** Tue Oct 11, 2011 11:53 pm

More cuboid philosophizing:

Tony Fisher's Cuboid Transformations show us how to reduce an axis by a cubie, allowing you to derive from the 3x3x3 the smaller true cuboids 2x3x3, 2x2x3 and 2x2x2.

Given any of these cores, you can use the extension techniques (here, here, here, etc) of carving a circular track into a face and inserting cubies with feet to extend any single axis by two more cubies and producing a larger true cuboid:

3x3x3 -> 3x3x5 (mass produced, but non-proportional)
2x3x3 -> 3x3x4 (mass produced)
2x3x3 -> 2x3x5 (hand-made)
2x2x3 -> 2x3x4 (printed)
2x2x3 -> 2x2x5 (printed)
2x2x2 -> 2x2x4 (mass produced)

And of course you can repeat the trick - on that same axis - until the feet become too thin/weak:

3x3x3 -> 3x3x5 -> 3x3x7 (mass produced, but non-proportional)
2x3x3 -> 3x3x4 -> 3x3x6 (mass produced)
2x3x3 -> 2x3x5 -> 2x3x7 (hand-made)
2x2x3 -> 2x3x4 -> 2x3x6 NOT YET MADE <-- hey opportunity here!
2x2x3 -> 2x2x5 -> 2x2x7 (surely someone has one made this way...)
2x2x2 -> 2x2x4 -> 2x2x6 (printed)

You can keep going. And many (I'm looking at you, Traiphum!) have. You can also start with higher order cubes as Tony did with the 4x4x6, and many others followed; even Ayi's wonderful 4x4x5 and upcoming 5x5x4 are, conceptually, "Fisher cuboid transforms" of the 5x5x5. As anyone who's ever even assembled one knows, the engineering challenge is significant even if it sounds easy on paper.

traiphum · **Posted:** Wed Oct 12, 2011 1:56 am

so start with marked "NOT YET MADE"
How about 4x5x6? :wink:

PotatoSpades22095 · **Joined:** Sun Sep 28, 2008 9:56 pm

Joshua Bell wrote:

PotatoSpades22095 wrote:

Can you make a video showing all of them, and showing that each is fully functional?

Then you'd see my messy house.

How about this instead:

Cuboids - Checkerboarded by inexorabletash, on Flickr

I forgot to scramble the 1x1xNs. Sorry - I promise they're fully functional. Even the 1x1x1.

I bet you just replaced the stickers

Well, i believe you that they are fully functional, what I meant is that I would just love to see them all move, and hear the sound they make

Joshua Bell · **Posted:** Fri Nov 25, 2011 3:49 pm

Two new additions, so new pictures:

Cuboids (this time it's personal) by inexorabletash, on Flickr

1x1xN:
1x1x1 Silly Custom
1x1x2 Silly Custom
1x1x3 Silly Custom

2x2xN:
2x2x1 Minimis by VeryWetPaint (Shapeways)
2x2x2 Rubik's Pocket Cube
2x2x3 Okamoto's Slim Tower (Gentosha)
2x2x4 Rubik's Tower (Megahouse)

3x3xN:
3x3x1 Okamoto's Floppy Cube (Gentosha)
3x3x2 QJ
3x3x3 Rubik's Cube
3x3x4 Cube4You
3x3x5 Custom (from WitEden Super 3x3x3)
3x3x6 WitEden
3x3x9 WitEden

4x4xN:
4x4x2 Ola Jansson (Shapeways)
4x4x3 Garrett Ong (Shapeways)
4x4x4 Rubik's Revenge
4x4x5 Ayi's Toy 445
4x4x6 TomZ (Shapeways)

5x5xN:
5x5x4 Ayi's 554 -- NEW!
5x5x5 Rubik's Master

Higher Order NxNxN:
6x6x6 V-Cube 6
7x7x7 V-Cube 7

Irregulars:
1x2x3 Custom
1x2x4 Tanner Frisby
2x3x4 Garrett Ong (Shapeways)
2x3x5 Custom (from QJ 2x3x3)
3x4x5 TomZ (Shapeways)
4x5x6 TomZ (Shapeways) -- NEW!

I finally restickered the Gentosha puzzles and my 1x2x3 to match.

clauswe · **Joined:** Tue Dec 09, 2008 1:05 am

I love this picture.

It looks fantastic!!!

grigr · **Joined:** Mon Jun 30, 2008 8:38 pm **Location:** Russia

You need my Slim Cube

Aether13 · **Joined:** Sat Feb 05, 2011 1:06 pm

I am beyond jealous of your cuboid collection, unfortunately the only one I have is the 3x3x4 ):. Oh well that will change soon enough haha.

77mouser · **Posted:** Tue Nov 29, 2011 8:10 am

Cool cuboids! Now the real question is-have you solved all of them yet?

I <3 Cuboids!

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