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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Mon Dec 29, 2008 11:47 pm 
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I'm pretty sure he said it was a 4-armed spider, so it only turns on 4 axes.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Tue Dec 30, 2008 2:38 pm 
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Simply excellent.


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Tue Dec 30, 2008 7:58 pm 
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Drewseph wrote:
Truth is, its just a 4-armed core, on an axis, and adjusted cuts to remove the centers and corners.


So it is a master tetrahedron with each face looks like the following, and when we cut the four corners along the red dashed lines, the puzzle will become a face-turning octahedron. So this puzzle is identical to face-turning octahedron mathematically. Please correct me if I am wrong.

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face3.jpg
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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Jan 01, 2009 6:34 pm 
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@sokoban
I came up with the same conclusion. :)
The praxis cube is mathematically identical to that new face-turning octahedron.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sun Jan 04, 2009 2:34 pm 
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Absolutely Stunning, this is probably my favorite puzzle made in 2008. Definately saving the best for last. Amazing job.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Jan 09, 2009 3:10 pm 
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I was lucky enough to get a chance to play with Drew's Master Skewb, Praxis, and ET (v2)... And I just wanted to tell everyone that they are all absolutely PERFECT. They cut corners like it's their job. We also took apart the Praxis, and holy god that puzzle is frightening, and should be kept away from small children. I highly recommend playing with these things if you get the chance! They're incredible.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Jan 09, 2009 3:14 pm 
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This puzzle is amazing! I can simply not imagine how you come up with all these amazing ideas, Drew. Congratulations on another successful build. :D

-Grant

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Wed Feb 11, 2009 3:13 pm 
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Scott Bedard wrote:
I was lucky enough to get a chance to play with Drew's Master Skewb, Praxis, and ET (v2)... And I just wanted to tell everyone that they are all absolutely PERFECT. They cut corners like it's their job. We also took apart the Praxis, and holy god that puzzle is frightening, and should be kept away from small children. I highly recommend playing with these things if you get the chance! They're incredible.


Are we likely to see Drew's Master Skewb or Praxis up on http://www.bedardpuzzles.com any time soon?

Carl

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Wed Feb 11, 2009 4:05 pm 
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After I finish the DRD orders, yes you will

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 12:23 am 
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Drew, I posted this question earlier, but didn't get a reply: are there any chances that you might ever make a "non-confusing" version of this puzzle, which isn't "axis-ed" (i.e. every cut is centered around a corner)?


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 12:42 am 
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and I didn't reply because that's a pretty .... well, ridiculous question, since it wouldn't be a Praxis cube at that point. so no, there is only one design for the Praxis cube.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 1:24 am 
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How much will one of these set us back?

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 1:32 am 
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I don't know, I haven't decided

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 10:04 am 
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Drewseph wrote:
and I didn't reply because that's a pretty .... well, ridiculous question, since it wouldn't be a Praxis cube at that point. so no, there is only one design for the Praxis cube.


Well, of course it wouldn't be a Praxis cube, but it would still be a nifty puzzle, whatever you decided to call it. >_>


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 6:19 pm 
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Why the name Flambore? I don't see much relevence from google... So, why Praxis?


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 6:26 pm 
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Jared wrote:
Drewseph wrote:
and I didn't reply because that's a pretty .... well, ridiculous question, since it wouldn't be a Praxis cube at that point. so no, there is only one design for the Praxis cube.


Well, of course it wouldn't be a Praxis cube, but it would still be a nifty puzzle, whatever you decided to call it. >_>




It wouldn't exist :lol:

The praxis in "un axis-ed" cube form is somewhere between a Master Skewb and a Dino cube. It's a [Master Skewb MINUS the eight corners] or a [Dino cube PLUS all of those other Master Skewb pieces :) ]
It couldn't exist by convential means. :mrgreen:

Of course you could cheat a little and make it like this 8-)

In octahedron form, I believe it is this.

Unless I'm mistaken... :roll:

Peace


Last edited by Allagem on Thu Feb 12, 2009 6:35 pm, edited 2 times in total.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 6:31 pm 
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Politely Owned wrote:
Why the name Flambore? I don't see much relevence from google... So, why Praxis?




Ummm.... there are two things wrong with this question....

Re-read the first post on page 1 and see if you can redeem yourself :wink:

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 11:13 pm 
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I can't believe I just did that....
UGH....

That makes me so sad that I just made such a horrible life mistake. Please let me be forgiven and relieved of that horrible act.


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Thu Feb 12, 2009 11:37 pm 
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Allagem wrote:
It couldn't exist by convential means. :mrgreen:


This confuses me. If it can exist when "axised", why can't it when not?


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 12:04 am 
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I haven't looked into it too much, but I would assume that the Praxis Cube wouldn't be possible either without the spherical cutting planes (notice the 2 different corners are the meetings of three cutting "planes", if you were to "straighten" the spherical cuts out, they wouldn't meet at the corner in the same way)

I was just pointing out that the unconfusing version of the puzzle - nominally a cube with straight cuts is not perfectly realizable.
You could probably make the gelatin brain's applet puzzle I pointed out perfectly cubical if you used spherical cuts too. In that case, that would be the un-axised version.

And @PolitelyOwned - I'm sure we can all forgive you, everyone makes mistakes :mrgreen:
and am I the only one that sees the irony of your username here? :lol:

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 12:46 am 
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What do you mean by "axis-ed" or "un-axised"? I cannot understand it, would you please explain a little? Thank you.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 1:23 am 
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sokoban wrote:
What do you mean by "axis-ed" or "un-axised"? I cannot understand it, would you please explain a little? Thank you.


Well, by 'axis-ed' we mean that the puzzle is turned inside it's shape. The axis cube for example is just a 3x3, but it has been turned inside the cube, which makes it change shapes in a rather complicated manner. The praxis cube is a masters skewb that has also been axised and had it's corners/centers hidden. We were discussing what one that hasn't been 'axis-ed' but still had some parts hiddenl would be like.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 5:23 am 
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..... Maybe I've been avoiding this conversation because it might be something I'm working on ......

HINT.... HINT

(yes you guys were getting too persistent)

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 6:00 am 
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TomZ wrote:
Well, by 'axis-ed' we mean that the puzzle is turned inside it's shape. The axis cube for example is just a 3x3, but it has been turned inside the cube, which makes it change shapes in a rather complicated manner. The praxis cube is a masters skewb that has also been axised and had it's corners/centers hidden. We were discussing what one that hasn't been 'axis-ed' but still had some parts hiddenl would be like.


Thanks for your explanation. I see it now.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 2:39 pm 
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Okay, so you may have noticed I was reluctant to talk about the practicality of an non-Axis'd Praxis cube.

Truth is its been ready since mid December, but before I optimized the design I axis-ified it and fell in love. that became the Praxis cube.

So your persistence has pushed me to jump on it and optimize it this morning....
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will be printed next week.


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Rex_Cube.jpg
Rex_Cube.jpg [ 44.89 KiB | Viewed 4430 times ]

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 2:46 pm 
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Ooh
Gelatinbrain 3.2.6!

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 2:47 pm 
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I love it! Thats really an appealing cube Drew! WOW

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 2:51 pm 
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Beautiful puzzle Drew! I love it and can't wait to give it a spin :D

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 2:52 pm 
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Drewseph wrote:
Okay, so you may have noticed I was reluctant to talk about the practicality of an non-Axis'd Praxis cube.

Truth is its been ready since mid December, but before I optimized the design I axis-ified it and fell in love. that became the Praxis cube.


NICE!!!! I'm in love... and I think I personally like the pre-axis-ified version more. I can't wait to see the real puzzle.

So it appears Allagem was at least half correct...

Allagem wrote:
Of course you could cheat a little and make it like this 8-)

In octahedron form, I believe it is this.

Unless I'm mistaken... :roll:


Is he correct about the octahedron form as well? His link to the one on youtube is my first introduction to that particular puzzle and I'd LOVE to get my hands on that variant as well.

Boy... so many new puzzles... and I WANT them all. Looks like its time to start looking for a second job. :D

Keep up the GREAT work!!!
Carl

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 4:15 pm 
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Idea:
I was thinking about paired puzzles, and this has a simple pair. It would be superficially the same, but turn on the closer of the two cuts. The centers wouldn't move.
The puzzle would be simpler to solve, but it might be neat to show off as a pair.


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 5:05 pm 
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Would this be considered something along the lines of a master dino cube?

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 5:45 pm 
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Beautiful....

I guess you might call this a "deep-cut" dino cube.

-Pi

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 5:54 pm 
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Isnt it a cubic face turning octahedron?

Well when you put a triangular face on a corner piece on each side....

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 5:57 pm 
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Nobody gets it even after the first page. Its not a face turning octahedron, its not a deep cut dino cube.

Its just a Master Skewb

however apparently the mechanism can be altered to function like a face turning octahedron?

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Fri Feb 13, 2009 5:59 pm 
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Drewseph wrote:
however apparently the mechanism can be altered to function like a face turning octahedron?


Then try to make a octahedron from it in 3d, to see result:D

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 2:21 am 
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Drewseph wrote:
Nobody gets it even after the first page. Its not a face turning octahedron, its not a deep cut dino cube.

Its just a Master Skewb

however apparently the mechanism can be altered to function like a face turning octahedron?


Well I would argue that these two puzzles (praxis and the new one) ARE different from a Master Skewb. Both of these puzzles have...42 pieces, right?? The Master Skewb has 50. The difference is the eight corners of the Master Skewb. In the Praxis and the new puzzle, the rotation planes are curved to eliminate these corner pieces. Which is why I said they couldn't be made by convential means. *I consider the spherical rotation planes non-convention, though I guess that is more of an opinion*

And as far as the deep cut dino goes - I claim the Master Skewb="deeper" cut dino cube.
I also claim that Master Skewb - 8 corners = face-turning octahedron, at least mathematically(same pieces in same orbital relationship)

a quick definition before my final claim- lets say the order of a puzzle is how many independent layers are connected by a single axis to the core of the puzzle, that is 3x3x3 = order 1. 5x5x5 = order 2. I know most people already know this term but I just wanted to clarify...

Ok finally, a tricky truth that took me awhile to realize:

Octahedral puzzle of order x = tetrahedral puzzle of order 2x. (provided both are as deep cut as possible, ex: Master Skewb = master tetrahedron)

It is my understanding that Drew made all of these puzzles off a tetrahedral core - order 2, which is why he so quick to oppose the deep-cut dino theory. Okamoto, I think, made his Master Skewb out of a rainbow cube -> octahedral core. In Drew's Master Skewb thread, I mentioned that I have a working design for a Master Skewb (I know, I'm working on it.... :oops: ) Mine is octahedral based, but of only order 1.

So unless I have made a mistake somewhere, I believe that
the Master Skewb and the Master Tetrahedron are mathematically identical
and
the Praxis Cube, the un"axised" praxis, the face turning octahedron, gelatinbrain's 3.2.6, and Master Skewb without corners are all mathematically identical

Better? :P

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 2:43 am 
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Quote:
Both of these puzzles have...42 pieces, right?? The Master Skewb has 50


the master skewb has 55, this and the praxis have 51, no center caps.

I agree now that you have explained why. I just won't call the mech an octahedral mech, since it was designed for the Master Tetrahedron.

I do understand where you are coming from now though. good input!

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 3:23 am 
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Drewseph wrote:
Allagem wrote:
Both of these puzzles have...42 pieces, right?? The Master Skewb has 50


the master skewb has 55, this and the praxis have 51, no center caps.



I think Allagem mean visible pieces, or mathematical pieces.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 10:25 am 
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Very interesting discussion Allagem... I love this matematical stuff.
Allagem wrote:
I also claim that Master Skewb - 8 corners = face-turning octahedron, at least mathematically(same pieces in same orbital relationship)
I can't see that in my head. I'll accept it as true and see if I can make a picture that will prove it to me. In cases like this a picture is worth 1000 words.
Allagem wrote:
a quick definition before my final claim- lets say the order of a puzzle is how many independent layers are connected by a single axis to the core of the puzzle, that is 3x3x3 = order 1. 5x5x5 = order 2. I know most people already know this term but I just wanted to clarify...
Arg... I'm one of the few that isn't familiar with that term. Is there a thread you could point me to so I could learn more? For example the 3x3x3 has 3 layers connected by a single axis to the core so I assume the key is how many of them are "independent"? I would have guessed 2 and that a 2x2x2 would have 1. I want to understand but I also don't want to derail this thread about this great puzzle.
Allagem wrote:
Octahedral puzzle of order x = tetrahedral puzzle of order 2x. (provided both are as deep cut as possible, ex: Master Skewb = master tetrahedron)
I think I follow. Are you saying the master tetrahedron is NOT equal to the Type A Master Skewb (or Dino Cube) because it isn't as deep cut at the other Master Skewbs seen here?
http://puzzle3d.hp.infoseek.co.jp/masterskewb.html
Allagem wrote:
It is my understanding that Drew made all of these puzzles off a tetrahedral core - order 2, which is why he so quick to oppose the deep-cut dino theory. Okamoto, I think, made his Master Skewb out of a rainbow cube -> octahedral core. In Drew's Master Skewb thread, I mentioned that I have a working design for a Master Skewb (I know, I'm working on it.... :oops: ) Mine is octahedral based, but of only order 1.
A light goes off... So two completely different ways to make a Master Skewb. In Drew's Master Skewb thread he stated:
Drewseph wrote:
Type D results in the corners having hardly anything to hold onto the the center core, the mechanism becomes way too fragile in imo to have invested $400 into. the main issue is that the corners neck becomes thinner than the screw hole. the hole itself is so small, I prefer the neck to reach around the hole so the plug I insert into it is not visible once the corner caps are inserted.
I wonder... Is this only an issue with the tetrahedral core design? Or do you face a similiar issue with your octahedral core design Allagem?
Allagem wrote:
Praxis Cube, the un"axised" praxis, the face turning octahedron, gelatinbrain's 3.2.6, and Master Skewb without corners are all mathematically identical
The biggest issue I have here is visualizing these as the same. The Praxis Cube and the Unaxised Praxis both have spherical rotational cuts. The face turning octahedron, gelatinbrain's 3.2.6, and Master Skewb have planar rotational cuts. Going from the Unaxised Praxis to gelatinbrain's 3.2.6 is obvious so I'm sure you are correct but I'm really curious what the Unaxised Praxis would look like in an octahedral shell, spherical rotational cuts and all? Would it be obvious is was a face turning octahedron? Drewseph would it be too much to ask for a pretty picture of that variant? If it looks as pretty as I think it might I'd hope its another puzzle you'd consider making down the road.

Thanks,
Carl

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 1:05 pm 
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wwwmwww wrote:
Very interesting discussion Allagem... I love this matematical stuff.
Allagem wrote:
I also claim that Master Skewb - 8 corners = face-turning octahedron, at least mathematically(same pieces in same orbital relationship)
I can't see that in my head. I'll accept it as true and see if I can make a picture that will prove it to me. In cases like this a picture is worth 1000 words.


Best way to think about it is that a Skewb Diamond is a 2 layer face turning octahedron. A Face Turning Octahedron is a 3 layer face turning octahedron, making it a Master Skewb Diamond.

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Allagem wrote:
a quick definition before my final claim- lets say the order of a puzzle is how many independent layers are connected by a single axis to the core of the puzzle, that is 3x3x3 = order 1. 5x5x5 = order 2. I know most people already know this term but I just wanted to clarify...
Arg... I'm one of the few that isn't familiar with that term. Is there a thread you could point me to so I could learn more? For example the 3x3x3 has 3 layers connected by a single axis to the core so I assume the key is how many of them are "independent"? I would have guessed 2 and that a 2x2x2 would have 1. I want to understand but I also don't want to derail this thread about this great puzzle.


I think Allagem means the number of layers connected to the core by one "arm". A 3x3x3 has one layer per arm, plus the middle. A 5x5x5 has 2. :wink:

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 3:03 pm 
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Wow, that "Rex_Cube" is going to look awesome when it's built! Those (I don't know what to call them) spherical cuts just make this one look beautiful. It reminds me of a butterfly. :D

-Jon

*I'm not going to argue about what this is or isn't mathematically equal to. Drew designed it, so I think he knows exactly what it is.*

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 6:17 pm 
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wwwmwww wrote:
Allagem wrote:
I also claim that Master Skewb - 8 corners = face-turning octahedron, at least mathematically(same pieces in same orbital relationship)
I can't see that in my head. I'll accept it as true and see if I can make a picture that will prove it to me. In cases like this a picture is worth 1000 words.

That is a hard picture to make, but I'll certainly try :P See the attachment
wwwmwww wrote:
Allagem wrote:
a quick definition before my final claim- lets say the order of a puzzle is how many independent layers are connected by a single axis to the core of the puzzle, that is 3x3x3 = order 1. 5x5x5 = order 2. I know most people already know this term but I just wanted to clarify...
Arg... I'm one of the few that isn't familiar with that term. Is there a thread you could point me to so I could learn more? For example the 3x3x3 has 3 layers connected by a single axis to the core so I assume the key is how many of them are "independent"? I would have guessed 2 and that a 2x2x2 would have 1. I want to understand but I also don't want to derail this thread about this great puzzle.

I also don't want to hijack this thread any more than I kind of already have....(sorry Drew! :oops: )
Basically what matters is how many layers are out from the core of the puzzle. The 2x2x2 is tricky because its core is hidden. I would say a 2x2x2 is really a 3x3x3 in disguise so both are order 1.
wwwmwww wrote:
Are you saying the master tetrahedron is NOT equal to the Type A Master Skewb (or Dino Cube) because it isn't as deep cut at the other Master Skewbs seen here?
http://puzzle3d.hp.infoseek.co.jp/masterskewb.html

Correct :) Although I think the pieces of the dino cube ARE equal to certain pieces of the Master Tetrahedron (the diamond shaped ones between a center and a corner :wink: ) Basically as you build through the different cut depths, certain pieces on each puzzle match eachother and by the end (deep cut as possible) they all match up.
wwwmwww wrote:
So two completely different ways to make a Master Skewb.

Yep! There's no doubt about it :)
wwwmwww wrote:
In Drew's Master Skewb thread he stated:
Drewseph wrote:
Type D results in the corners having hardly anything to hold onto the the center core, the mechanism becomes way too fragile in imo to have invested $400 into. the main issue is that the corners neck becomes thinner than the screw hole. the hole itself is so small, I prefer the neck to reach around the hole so the plug I insert into it is not visible once the corner caps are inserted.
I wonder... Is this only an issue with the tetrahedral core design? Or do you face a similiar issue with your octahedral core design Allagem?

I'm not sure of the details of Drew's design, but my design does not have this problem at all. As a trade-off though, mine requires more pieces :?
wwwmwww wrote:
I'm really curious what the Unaxised Praxis would look like in an octahedral shell, spherical rotational cuts and all? Would it be obvious is was a face turning octahedron? Drewseph would it be too much to ask for a pretty picture of that variant? If it looks as pretty as I think it might I'd hope its another puzzle you'd consider making down the road.

That's a good question! 8-)
I guess it would be like a face-turning octahedron but with curvy cuts? :P

Peace

Edit: I notice that I may be using the term order differently than some... The relationship works with the other interpretation of order where a 3x3x3 is order 3 and a skewb is order 2. In this scheme then a Master Skewb, regardless of how it is built, is of order 3. I personally don't support this ordering scheme, but let's stay on topic on this thread :)


Attachments:
File comment: A blue Master Skewb and red Face Turning Octahedron super-imposed on eachother. The green piece is a Master Skewb corner that has no counterpart on the Face Turning Octahedron
Master Skewb Octahedron Relationship.jpg
Master Skewb Octahedron Relationship.jpg [ 41.49 KiB | Viewed 4106 times ]
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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 6:40 pm 
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Wow, this discussion's way over my head...Drew, if you want to send me samples of all of your puzzles, I can play with them and tell people how they turn.
:D

j/k (obviously), I can't wait to see the new version completed!


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 8:19 pm 
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So should we start calling the FTO the "Master Skewb Diamond" then? (That at least has a sort of a ring to it...)

(Of course if the cuts are shallower on the FTO then you do in fact have those corner pieces visible - Okamoto-san's Dino Octa puzzle.)


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 8:47 pm 
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Allagem wrote:
So unless I have made a mistake somewhere, I believe that
the Master Skewb and the Master Tetrahedron are mathematically identical
Surprising (to me at least) but true! But of course they differ in which pieces are visually distinct or require orientation. The 24 "outer center" squares of the Master Skewb come in 6 sets, 4 on each face, and their position within each set doesn't matter -- but the equivalent pieces of the Master Tetrahedron split into two: 4 sets, 3 on each face, whose position within each set doesn't matter (the single color quadrilaterals); and the other 12 which have set positions (the 2-colored pieces adjacent to the corners). The orientation of all 8 corners of the Master Skewb matters, but the orientation of only 4 of the equivalent pieces of the Master Tetrahedron (the corners) matters.
Allagem wrote:
and
the Praxis Cube, the un"axised" praxis, the face turning octahedron, gelatinbrain's 3.2.6, and Master Skewb without corners are all mathematically identical
The corners of the face turning octahedron need orienting correctly, whereas the equivalent pieces of the Rex Cube, Gelatinbrain 3.2.6 (Fat Skewb), and cornerless Master Skewb (the 6 center squares, one per face) do not. So the octahedron is a "super" version of those puzzles, and the Praxis Cube is the "ultimate" version in that every piece has to be positioned exactly (I think).


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 8:58 pm 
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Julian, the shape makes no difference to the solution. The only difference is in the stickering schemes. If any one way of stickering was kept for all shapes, they would have the same solution. I can't make a pretty picture or anything, but perhaps someone else can if you still don't understand.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sat Feb 14, 2009 9:35 pm 
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Allagem, your picture is awesome.

Both FTO and the rex cube are master skewbs without 8 corners. The FTO is obtained by cutting the cornners, and the rex cube is obtained by adjusting the planar-cuts to spherical-cuts. Two different approach with the same outcome, interesting.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sun Feb 15, 2009 1:24 am 
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Jared wrote:
So should we start calling the FTO the "Master Skewb Diamond" then? (That at least has a sort of a ring to it...)

(Of course if the cuts are shallower on the FTO then you do in fact have those corner pieces visible - Okamoto-san's Dino Octa puzzle.)



Hmmm... :|
Be careful here, because while you are correct in saying that the shallower cuts of an FTO produce the Dino Octa, you can also go the other direction. Deepening the cuts of an FTO produce this puzzle which does include the Master Skewb corners; I think this should be called a Master Skewb Diamond.

(Plus people seem to really like pictures :lol: )

Peace


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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sun Feb 15, 2009 4:54 am 
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That's definitely it. Building this also doesn't require canging the mech in any way. It would just be the mod of a Master Skewb. Truncate the corners and build the rest up. Of course it would be pretty big then, even if made from Drew's Master Skewb that has larger corners than Mr. Okamot's. It is beautiful though.

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 Post subject: Re: Drewseph's Praxis Cube
PostPosted: Sun Feb 15, 2009 7:04 am 
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Danny Devitt wrote:
Julian, the shape makes no difference to the solution. The only difference is in the stickering schemes. If any one way of stickering was kept for all shapes, they would have the same solution.
With the exception of the Praxis Cube, my post was pointing out differing solution requirements due to differing color/stickering schemes, and I agree with you.

Regarding "the shape makes no difference to the solution", first consider a Golden Cube. The stickering scheme is a single color, but the Golden Cube obviously isn't equivalent to a single-color Skewb solving-wise. The Golden Cube requires every piece to be correctly permuted and oriented (the equilateral triangle would be an exception, but for the fact you can't have a single misoriented Skewb corner), just like a Skewb Ultimate, not because of its stickering scheme but because of its shape.

Now the 6 large, curved kite-shaped pieces of the Praxis Cube, which have one sticker color, are equivalent to 6 of the 12 two-colored edges of a normal Master Skewb (I think). Following the coloring scheme of the Praxis Cube, those Master Skewb pieces would be one color, and it wouldn't matter if pairs of them were flipped or not, but it does matter with the Praxis Cube, as the kites would be looking very upside-down and unsolved. Hope this makes sense and sorry if I'm wrong -- I do find the Praxis Cube a confusing puzzle to look at!


Last edited by Julian on Sun Feb 15, 2009 7:27 am, edited 1 time in total.

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