Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum

It is currently Tue Jul 22, 2014 5:31 am

All times are UTC - 5 hours



Post new topic Reply to topic  [ 23 posts ] 

What should we call these?
bites 11%  11%  [ 1 ]
decepticuts 33%  33%  [ 3 ]
intersections of revolved solids 33%  33%  [ 3 ]
some mathematician has already named these _______ 0%  0%  [ 0 ]
cut type _______ 22%  22%  [ 2 ]
Total votes : 9
Author Message
 Post subject: What should we call these?... Spin off of Oskar's Oh Cube
PostPosted: Fri Jun 24, 2011 8:45 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Ok... I've done it again and taken another good thread so far off course that I feel the need to start a new topic to get over my guilt. Let's use this thread to post new pics, videos, how-to's, and discussions about this new way to dice up 3D solids and make very deceiving twisty puzzles.

I'm talking above the type of "cuts" Oskar has used in these puzzles:

http://www.shapeways.com/model/50089/kilominx.html?gid=sg13603
http://www.shapeways.com/model/49957/slice_kilominx.html?gid=sg13603
http://www.shapeways.com/model/40561/redi_cube.html?gid=sg13603
http://www.shapeways.com/model/40559/fadi_cube.html?gid=sg13603
http://www.shapeways.com/model/139101/oh_cube.html?gid=sg13603
http://www.shapeways.com/model/237478/mosaic_block.html?gid=sg13603

And Muffet has used in this one:

Helicopter Dodecahedron

Note, if you pick one of the last two options you must post to fill in the blank.

Carl

_________________
-
Image

Image


Last edited by wwwmwww on Fri Jun 24, 2011 11:18 pm, edited 2 times in total.

Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 9:37 pm 
Offline
User avatar

Joined: Sun Jun 13, 2010 1:00 am
Location: Colorado
I think they are just cuts. Nothing shows them as anything else. However I do agree they should be classified as a type of cut, maybe sketch, form, stlye, or trace cuts, refering to beign used to make surface designs.

_________________
My Shapeways Shop
My YouTube Videos
My Museum Puzzles


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 9:42 pm 
Offline
User avatar

Joined: Tue Mar 10, 2009 7:06 pm
Location: Nowhere in particular.
Here we go again! :lol:

I don't know about anyone else, but I don't like any of those names. I also think I speak for just about everyone when I say "Oskaring" isn't going to cut it, especially since it could describe like 100 different things. Personally, I think the name should have something to do with the outer surfaces of the puzzle "going under" the other surfaces during a turn, as all of the puzzles you've listed seem to share that common trait. (That being said, could the icosaix be classified in this same group?)

Another option could be to call them parabolic cuts, assuming they all share the cut type shown by TomZ in his latest video. Although the name "conic" cuts is already in use, parabolic cuts is still an unused term which would accurately describe this cut.

_________________
~Kapusta

PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

Current Goals:
7x7 sub 6:30
4x4 sub 1:10


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 10:08 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
PuzzleMaster6262 wrote:
I think they are just cuts. Nothing shows them as anything else.
I guess that depends on how you define cut.
PuzzleMaster6262 wrote:
However I do agree they should be classified as a type of cut, maybe sketch, form, stlye, or trace cuts, refering to beign used to make surface designs.
Fair enough... I'm open to calling them a type of cut but I'm not really happy with any of the names that have been proposed so far.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 10:50 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Kapusta wrote:
Here we go again! :lol:
Sorry... I love asking questions.
Kapusta wrote:
I don't know about anyone else, but I don't like any of those names.
I'm not totally happy with any of them either. So I'm open to write in votes as well.
Kapusta wrote:
I also think I speak for just about everyone when I say "Oskaring" isn't going to cut it, especially since it could describe like 100 different things.
Too true. Oskaring is now synonymous with breaking the universe.
Kapusta wrote:
Personally, I think the name should have something to do with the outer surfaces of the puzzle "going under" the other surfaces during a turn, as all of the puzzles you've listed seem to share that common trait. (That being said, could the icosaix be classified in this same group?)
Yes... yes it is. Another good catch. That is clear to see in this pic.
Attachment:
Icosaix.jpg
Icosaix.jpg [ 42.41 KiB | Viewed 3520 times ]

Its exactly that "Curved cut resulting in straight cuts at the surface" that we are talking about.
Kapusta wrote:
Another option could be to call them parabolic cuts, assuming they all share the cut type shown by TomZ in his latest video.
The one in his post had a parabolic cross section... not sure about the one in his video. But even that one isn't a parabolic cut. That would be like calling a torus a circle cut because its a circle revolved about an axis.

This is what I'd call a parabolic cut.
Image
or maybe this
Image
Kapusta wrote:
Although the name "conic" cuts is already in use, parabolic cuts is still an unused term which would accurately describe this cut.
I'd disagree. There may be no twisty puzzles with parabolic cuts (not sure about that) but that term is pretty self explanatory.
Let's go back to this picture Tom posted for the Oh Cube.
Attachment:
tomscut.png
tomscut.png [ 293.92 KiB | Viewed 3520 times ]

This 2D surface is a cut... I won't argue with that. What makes this different from other cuts? Let's look at the planar cut that cuts a 2x2x2 in half. Note each of the cuts divides the cube into two pieces by itself. The horizontal cut divides the puzzle into a top half and a bottom half. How many pieces does Tom's surface of revolution cut the puzzle into? Just one... This cut by itself still leaves each part of the cube connected to every other part. You need MORE then this surface to "cut" the puzzle into pieces. For the purposes of this discussion let's ignore the mech needed to hold the puzzle together. In other words a 2x2x2 is just a cube cut into 8 smaller cubes. Now go back to the Kilominx in Tom's video... what surfaces to you actually NEED to cut the dodecahedron into pieces? And are all those pieces still present in the final Kilominx? I don't think so. When you cut a cube into a 2x2x2 by forming 8 smaller cubes do you remove any volume from the puzzle?

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 11:15 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Correction... option (3) should read "intersections of revolved solids". The intersections of revolved 2D surfaces would be 1D curves and I want 3D solids. I've been playing with POV-Ray too much where a plane is treated as a half-space and a cube can be made as the intersection of 6 planes.

Here is also another pic which may be useful in this thread...

Image

Take away the white text which I added back in August 2006 and bonus points to anyone that can tell me the source of this image.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 11:23 pm 
Offline
User avatar

Joined: Tue Mar 10, 2009 7:06 pm
Location: Nowhere in particular.
So, correct me if I'm wrong, but is the shape of the "cut" a "one-sheeted hyperboloid?"

_________________
~Kapusta

PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

Current Goals:
7x7 sub 6:30
4x4 sub 1:10


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 11:46 pm 
Offline
User avatar

Joined: Sun Jun 13, 2010 1:00 am
Location: Colorado
Would you say the Fluffy Cube has these cuts? In my opinion it does because the cuts are altered for a specific external look.

I couldn't find links for it, I think they have been erased.

_________________
My Shapeways Shop
My YouTube Videos
My Museum Puzzles


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Fri Jun 24, 2011 11:54 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Kapusta wrote:
So, correct me if I'm wrong, but is the shape of the "cut" a "one-sheeted hyperboloid?"
For the Oh Cube... yes part of the cut is a one-sheeted hyperboloid. To actually cut the cube into pieces you'll need to add a cone to it. I believe that the volume that is removed from the puzzle is the intersection of several a one-sheeted hyperboloids. Is this surface still a one-sheeted hyperboloid on a Kilominx? Or a icosaix? I'm not sure that is true in general.

Carl

P.S. I'm now wondering if adding a cone to the cut is needed. The one-sheeted hyperboloid if extended to the surface of the puzzle in all directions does cut the cube into two pieces. You get an equator section which can be rotated around the rest of the cube. Is this the same as taking the Oh Cube and holding two opposite corners fixed and rotating the others around them? I'm not sure at the moment. Even if so I still think these cuts need to intersect in a way which would remove volume from the puzzle if you had more then one such cut.

_________________
-
Image

Image


Last edited by wwwmwww on Sat Jun 25, 2011 12:12 am, edited 1 time in total.

Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 12:02 am 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
PuzzleMaster6262 wrote:
Would you say the Fluffy Cube has these cuts? In my opinion it does because the cuts are altered for a specific external look.
No. Each cut in the Fluffy Cube by itself cuts the puzzle in two. A cube cut with 6 such cuts still cuts the cube into 27 volumes with no extra volume removed. In effect each of these cuts is doing nothing the planar cuts on a normal 3x3x3 isn't doing. Not to sell the Fluffy Cube short... its quite original in its own way.
PuzzleMaster6262 wrote:
I couldn't find links for it, I think they have been erased.
grigr said here that he had a reason to remove the Fluffy Cube.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 4:51 am 
Offline
User avatar

Joined: Tue Jul 08, 2008 3:39 pm
Location: Cornwall, United Kingdom
'Mercator Solids'.


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 5:02 am 
Offline
User avatar

Joined: Mon Mar 30, 2009 5:13 pm
How about "Intersecting Circular Ellipsoid cuts" (or "ICE cuts" for short 8-) ) - because that's essentially what they are, like intersecting/overlapping eggs that rotate around their long axis extending to each corner of the cube. The edge pieces are formed by the intersect of two overlapping eggs, while the centre pieces are formed by the intersect of four overlapping eggs. And the corner pieces comprise the part of each egg that does not intersect/overlap with any of the other 7 eggs. :D

... although these "eggs" must be somehow sculpted/distorted towards the surface to make the cuts appear straight in the Oh Cube, but still I think the mechanism is essentially based on "ICE cuts" as described above ...

_________________
If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 1:49 pm 
Offline
User avatar

Joined: Sat Mar 29, 2008 12:55 am
Location: WA, USA
well, if they are hyperboloid shaped... why don't we just call them hyperboloid cuts? Or, simply hyper-cuts?
Twisty puzzles seems to like words like that... super, master, ultimate, ultra. I think hyper-cuts will fit right in to everyday lingo.

_________________
"This is Pretty off-topic"

"You are actually more off topic than me, you mentioned something on topic in the Off Topic forum."

"You more so for discussing the on-topic "off-topic" topic in the off-topic forum."


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 2:50 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
wwwmwww wrote:
P.S. I'm now wondering if adding a cone to the cut is needed. The one-sheeted hyperboloid if extended to the surface of the puzzle in all directions does cut the cube into two pieces.

Ok... trying to answer this question I did some playing in paint.
Image
If you extend the surface of the hyperboloid you get cuts on the surface you don't want. So you CAN'T extend these cuts to the point they actually cut the cube into 2 pieces. So these cuts aren't the entire hyperboloid but finite pieces of the hyperboloid.
And with a bit more thinking I've convinced myself that the surfaces used to cut the Kilominx and Icosaix are hyperboloid too. Any straight line rotated around an axis I believe forms a hyperboloid. So this type of cut is a hyperboloid as long as the surface of the puzzles are planar.

To dig deeper I had to bring out the big guns as I can no longer draw this stuff in paint or even POV-Ray. So here is my sketch in SolidWorks.
Image
Its the black line and it was made coping the method from Tom's video. Had to go though it almost frame by frame in places to see what buttons he was pushing but I got there. I first made 8 copies of the hyperboloid cut by itself, 1 for each corner, and noted the cube was still in 1 connected piece. My initial thought was this hyperboloid cut defined the shape of the void which needed to be removed and that was it but if so then the void region should have been cut free from the cube with this process and it wasn't. Another failed assumption. So I need to add a cone to this hyperboloid to be able to actually cut the cube up into pieces. Note I'm NOT interested in the mech at this point. I'm just trying to understand how these cuts work and the simplest picture is usually the best. For example you can think of a 3x3x3 as a cube cut into 27 smaller cubes by 6 planes. That is enough to understand the volumes within a 3x3x3. So back to the Oh Cube... I revolve the above sketch and get this cut.
Image
I copy that cut to all 8 corners and I get the Oh Cube.
Image
These cuts cut the cube up into 104 pieces. Is that really the best I can do? Is it possible to use a more complex sketch and get fewer pieces? Maybe... Anyways here is a 3D pdf which has all 104 pieces in it... or at least it should.
http://www.wwwmwww.com/Puzzle/OhCube/OhCubeCuts.PDF
Playing with this pdf myself it appears a few pieces may be missing on the inside but maybe that's just me. I have no idea why anything would be missing.

So far this has shown me...
(1) Most of the volume that I thought needed to be a void appears to be able to be filled by the edge piece. So I'm now wondering if it is actually possible that this type of cut can be done without a void.
(2) This is even more complex than I thought... I was hoping for alot fewer pieces. 104 is still too complex for me to be able to understand all of them. And I'm still not convinced that all of them are needed.

Carl

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 3:12 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Justin wrote:
'Mercator Solids'.

Could you post a link? I'm not familiar with that term and google wasn't much help.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 3:22 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Kelvin Stott wrote:
... although these "eggs" must be somehow sculpted/distorted towards the surface to make the cuts appear straight in the Oh Cube, but still I think the mechanism is essentially based on "ICE cuts" as described above ...

An acronym could work... but the curves are hyperboloids, not ellipsoids. Since you must throw out part of the hyperboloid as you can't extent it to all surfaces we could called them finite hyperboloids. Now to actually cut the puzzle into pieces you need conical (and maybe spherical) cuts to finish the job. So maybe something like intersecting compound finite hyperboloid cuts... ICFHC... not much of an acronym. And yes, your picture is more or less correct but it glosses over the details I'm trying to understand. You've described that 'what' is being done. I want to understand the 'how'. Not sure anyone else want to follow me into my madness but I find this stuff fun.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 3:32 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
elijah wrote:
well, if they are hyperboloid shaped... why don't we just call them hyperboloid cuts? Or, simply hyper-cuts?
Twisty puzzles seems to like words like that... super, master, ultimate, ultra. I think hyper-cuts will fit right in to everyday lingo.

How about compound hyper cuts as you need more then just the hyperboloid surface in order to cut the puzzle into seperate pieces.? Maybe Cyper Cuts for short? The C should still sound like a K not an S.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 3:44 pm 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
PuzzleMaster6262 wrote:
elijah wrote:
next you should try to make a proportional one! So that it looks exactly like a normal 3x3!

The only problem is the corners wouldn't touch the core.

While playing around it SolidWorks it appears the corners get cut off well before the centeral layer becomes proportional. For it to be proportional you'd want the central layer width to be 33.333...% the width of the puzzle. A test at 22.222...% still cut the corners off. In the 3D PDF above its 16.666% and that worked.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 8:11 pm 
Offline
User avatar

Joined: Tue Jul 08, 2008 3:39 pm
Location: Cornwall, United Kingdom
wwwmwww wrote:
Justin wrote:
'Mercator Solids'.

Could you post a link? I'm not familiar with that term and google wasn't much help.

Carl
'Mercator' as in 'Mercator projection'. Mapping the curved lines that lie on a curved surface, onto a 2D plane so that they appear straight, parallel etc

http://en.wikipedia.org/wiki/Mercator_projection

Mercator solids/cuts/mappings/whatever. Although it's to do with maps, it's the same aesthetic result these puzzles are trying to achieve.


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Sat Jun 25, 2011 10:25 pm 
Offline
User avatar

Joined: Sun Jun 13, 2010 1:00 am
Location: Colorado
I'm in for Mercator cuts!

_________________
My Shapeways Shop
My YouTube Videos
My Museum Puzzles


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Wed Jun 29, 2011 7:27 pm 
Offline
User avatar

Joined: Sat Mar 29, 2008 12:55 am
Location: WA, USA
sounds good, Mercator or M-cuts for people like me who forget how to spell names like Mercator! :lol:

_________________
"This is Pretty off-topic"

"You are actually more off topic than me, you mentioned something on topic in the Off Topic forum."

"You more so for discussing the on-topic "off-topic" topic in the off-topic forum."


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Mon Aug 01, 2011 9:57 am 
Offline
User avatar

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Did we ever get closure on this topic? I saw it just came up again here. The more I think about it I'm leaning toward calling them hyperboloidal cuts. That is what they are. We have planar cuts, conical cuts, spherical cuts, etc. so why not just call these what they are? When I started this topic I wasn't aware of what their exact geometry needed to be.

Carl

_________________
-
Image

Image


Top
 Profile  
 
 Post subject: Re: What should we call these?... Spin off of Oskar's Oh Cub
PostPosted: Mon Aug 01, 2011 10:52 am 
Offline
User avatar

Joined: Sun Jun 13, 2010 1:00 am
Location: Colorado
Coming back to this topic over a month later I fully agree with Carl. Your last post really shows how mercator would be out of place with what we have already defined.

_________________
My Shapeways Shop
My YouTube Videos
My Museum Puzzles


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 23 posts ] 

All times are UTC - 5 hours


Who is online

Users browsing this forum: Google [Bot], Google Adsense [Bot] and 9 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  

Forum powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group