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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Fri Sep 25, 2009 12:26 pm 
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wwwmwww wrote:
This level of geometry NEEDS pictures.

I had the exact same thought. After the first three sentences I stopped and thought that the rest of this might as well be "blah blah blah" because there's no way I'm finishing this without pictures! :D

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Fri Sep 25, 2009 1:59 pm 
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lonogod wrote:
I had the exact same thought.
And I don't mean to just pick in stardust4ever either. When Bram said...

Bram wrote:
Pick a corner of the underlying megaminx. Glue in place the three face pieces which are closest to it and glue them in place so they can't spin. Then take the three face pieces which share two edges with pieces we just glued in place, and glue them in place as well. Finally, glue all edges which are shared by two of the face pieces we've glued, and all corners which are shared by three of them.

For the crystal layer, take the triangular piece above the corner you first picked and glue it, the three wedges it shares an edge with, and the three triangles on the other sides of those wedges, in place. Glue them to the mexaminx layer pieces which are glued in place as well.
I found myself wondering if this puzzle had more glue in it then plastic by this point. Everytime I try to picture what is glued to what it just sounds like everything is glued to everything else. This picture did help with the last bit though.

http://www.jaapsch.net/puzzles/sphere.htm?blue=45&symblue=5&red=28&symred=5&green=135&symgreen=5

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Fri Sep 25, 2009 4:20 pm 
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wwwmwww wrote:
I found myself wondering if this puzzle had more glue in it then plastic by this point. Everytime I try to picture what is glued to what it just sounds like everything is glued to everything else. This picture did help with the last bit though


Not quite. The way it works out you take a corner, glue all the pieces underneath that, then all the pieces underneath those, continue to core. It makes kind of a "pyramid" sticking out of the core.


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Fri Sep 25, 2009 5:15 pm 
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stardust4ever wrote:
I worked it out in my head mentally:



As you may well know, the Pyraminx crystal (PC) uses a megaminx core (MM). Just like the rube cube, the MM centers hold in the MM edges, which in turn hold down the MM corners. The MM centers and edges are rounded out like a sphere to give shape underneath the PC. The MM corners are extended to the PC corners. The PC edges are wedged underneath the PC corners. The Star Minx (SM) would likewise use an extended PC edge as the SM edge, which would hold it's other parts in. The SM edge holds the SM star points in place underneath them, which in turn hold the SM center in place. The SM face centers move exactly in the same manner as the pentagons on the Pentultimate (PU), so naturally, we extend the SM faces out and PU centers, but we cannot connect the PU corners without them falling off, as any grooves or notches we cut into the PU centers / corners to hold in place will be incompatible during mid-rotation (only reason this works for the Skewb is due to the even-sidedness of the square and the duality of the triangles). To alleviate this, grooves will be etched into the walls of the PU parts, and interlocking hidden tabs will be embedded into the grooves to lock in the parts and still allow PU corner/corner and center/center to glide together durning rotation. The SM edge pieces will have additional "spokes" that extend into the PU laters where the grooves iteresect, to prevent the interlocking PU tabs from colliding. Finally, for a fully functional Pentultimate, you need to prevent misaligned midsections in the SM region; this is easily attainable by simply locking six of the axes within the core in place, essentially blocking an entire hemisphere of the internal 12-axis.

Working outwards each layer starting from the MM: parts of the PC are trapped beneath MM parts; parts of the SM are trapped beneath PC parts; parts of the PU are trapped beneath SM parts; so that each layer locks in the layer outside itself.

So there you have it, a fully functional Pentultimate without the infamous "knucklehead" mechanism of the original (the twelve fully redundant floating layers were a bit convoluted :shock: ), though I dare say the number of moving parts required to achieve this is probably even greater :lol:

Cubic analogs:
MM (6 axis) <--> 3x3x3 (3 axis)
PU (6 axis) <--> skewb (4 axis)

Since their cubic counterparts don't even share the same number of axes, thus proves the intermediary stages of the cube version cannot exist :cry:


So basically, turn the 12-armed spider into a 6 armed spider? I really think we need a picture of this.

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 8:25 am 
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Sorry for not creating visuals, guys, but pentagonal objects are extremely difficult to make when you've only got the orthogonal axis (X, Y, Z) and right angles to work with.

When I said "block one whole hemisphere," I meant that one axis, and all the other five axis surrounding it, would be blocked. Alternately, a triangle of six axes could be used, as Bram proposed,
viewtopic.php?t=4229
but the recommended "pyramid of glue" would be unnessesary, as simply locking the aforementioned axes would demobilize said parts without need for extra glue.

While we are on the subject, who will volunteer to build this beast:
Attachment:
Ultimate Dodecahedron.PNG
Ultimate Dodecahedron.PNG [ 51.72 KiB | Viewed 1849 times ]
I think I'll call it the "Ultimate Pentagon Ball" :twisted:

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 9:51 am 
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stardust4ever wrote:
While we are on the subject, who will volunteer to build this beast:

I think I'll call it the "Ultimate Pentagon Ball" :twisted:


Oh... those are easy. I see your red, green, blue, and yellow ball and add in some white lines to boot.

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 10:17 am 
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stardust4ever wrote:
but the recommended "pyramid of glue" would be unnessesary, as simply locking the aforementioned axes would demobilize said parts without need for extra glue.


But that would make the puzzle "squishy". If there's an internal part that doesn't move at all relative to the core, there's no reason not to glue it down. Yes, technically just holding 6 axes would work, but we need to distribute the load otherwise the first time there's a lockup that you push a little too hard ...


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 10:48 am 
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wwwmwww wrote:
stardust4ever wrote:
While we are on the subject, who will volunteer to build this beast:

I think I'll call it the "Ultimate Pentagon Ball" :twisted:


Oh... those are easy. I see your red, green, blue, and yellow ball and add in some white lines to boot.

Image

Carl


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 7:45 pm 
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stardust4ever wrote:
Sorry for not creating visuals, guys, but pentagonal objects are extremely difficult to make when you've only got the orthogonal axis (X, Y, Z) and right angles to work with.

When I said "block one whole hemisphere," I meant that one axis, and all the other five axis surrounding it, would be blocked. Alternately, a triangle of six axes could be used, as Bram proposed,
viewtopic.php?t=4229
but the recommended "pyramid of glue" would be unnessesary, as simply locking the aforementioned axes would demobilize said parts without need for extra glue.

While we are on the subject, who will volunteer to build this beast:
Attachment:
Ultimate Dodecahedron.PNG
I think I'll call it the "Ultimate Pentagon Ball" :twisted:


A 4x4 minx/4x4 starminx/pyraminx crystal ball?

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 8:11 pm 
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elijah wrote:
A 4x4 minx/4x4 starminx/pyraminx crystal ball?


Actually I think it's a:
Green/Red: Gigaminx
Yellow: Hybrid Starminx
Blue: BigChop


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 10:49 pm 
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Sorry to be a pain, but can you give me the link to the program where you created this sphere visual. I know I have been there before, but I cannot find it.

stardust4ever wrote:

While we are on the subject, who will volunteer to build this beast:
Attachment:
Ultimate Dodecahedron.PNG
I think I'll call it the "Ultimate Pentagon Ball" :twisted:

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 10:53 pm 
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http://www.jaapsch.net/puzzles/sphere.htm


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Sep 29, 2009 10:57 pm 
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Thank you very much.

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Wed Sep 30, 2009 1:01 am 
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wwwmwww wrote:
stardust4ever wrote:
While we are on the subject, who will volunteer to build this beast:

I think I'll call it the "Ultimate Pentagon Ball" :twisted:


Oh... those are easy. I see your red, green, blue, and yellow ball and add in some white lines to boot.

Image

Carl
LOL :lol: I remember making one of those in high school. Not really a puzzle, but I started collecting all the rubber bands from our newspapers in a jar, and later started balling them up, until it got a little bigger than a soft ball. I don't know if you can drop kick the gigaminx like a V-Cube 7, but the band ball sure is a lot bouncier!!! :lol:

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Sun Oct 11, 2009 4:47 am 
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wwwmwww wrote:
How many solved states does this puzzle have? Since the centers can move and there are no 3 color corners I'm guessing its possible to solve the puzzle to a state that appears to be the mirror image of the starting state. If that's doable there should be atleast 2 solved states to this puzzle. Are there any other colorings of the dodecahedron possible where each face has the same neighbors but in another order? I don't think so but I'm not sure I can prove that. Maybe this puzzle has more then 2 solved states.

And a challenge... :!:

Assuming this puzzle has two solved states that are the mirror images of each other, what is the minimum number of moves required to get from one to the other?

Carl
Sorry for the late reply. I think a mirror image cannot be reached with the Starminx. If you pick any mirror plane that bisects the puzzle and cuts 4 faces in half, you'll have 2 edges that need to stay exactly as they are, 2 edges that stay in the same position but need to be flipped, and the other 26 edges need to swap places in pairs. 13 pair swaps -- an odd number -- hence impossible. If you tried to solve the Starminx into a mirror image state, the closest you could get is all the centers and corners correct, and all the edges correct but for 2 edges that need to swap places.


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Sun Oct 11, 2009 7:28 am 
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Julian wrote:
wwwmwww wrote:
I think a mirror image cannot be reached with the Starminx. If you pick any mirror plane that bisects the puzzle and cuts 4 faces in half, you'll have 2 edges that need to stay exactly as they are, 2 edges that stay in the same position but need to be flipped, and the other 26 edges need to swap places in pairs. 13 pair swaps -- an odd number -- hence impossible. If you tried to solve the Starminx into a mirror image state, the closest you could get is all the centers and corners correct, and all the edges correct but for 2 edges that need to swap places.
That would be one mean parity error :shock: resolve almost from scratch, funny, but also mean :lol: :cry: If it was mine, I'd probably just leave it that way and say I solved it! :roll:

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Sun Oct 11, 2009 8:38 am 
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Julian wrote:
Sorry for the late reply. I think a mirror image cannot be reached with the Starminx. If you pick any mirror plane that bisects the puzzle and cuts 4 faces in half, you'll have 2 edges that need to stay exactly as they are, 2 edges that stay in the same position but need to be flipped, and the other 26 edges need to swap places in pairs. 13 pair swaps -- an odd number -- hence impossible. If you tried to solve the Starminx into a mirror image state, the closest you could get is all the centers and corners correct, and all the edges correct but for 2 edges that need to swap places.
Wow!!! Thanks for that. A late reply is much better then no reply. This reads like a proof... but I noticed you started with "I think...". Mind if I ask how sure are you? Also the mention of "corners" puzzled me a bit. I assume you mean the face pieces which point toward the corners. Since they don't have assigned possitions on each faces (like the face centers on a 4x4x4) could two of those be swapped with the last two edges to make a mirror solution possible?

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Sun Oct 11, 2009 10:41 am 
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wwwmwww wrote:
Julian wrote:
Sorry for the late reply. I think a mirror image cannot be reached with the Starminx. If you pick any mirror plane that bisects the puzzle and cuts 4 faces in half, you'll have 2 edges that need to stay exactly as they are, 2 edges that stay in the same position but need to be flipped, and the other 26 edges need to swap places in pairs. 13 pair swaps -- an odd number -- hence impossible. If you tried to solve the Starminx into a mirror image state, the closest you could get is all the centers and corners correct, and all the edges correct but for 2 edges that need to swap places.
Wow!!! Thanks for that. A late reply is much better then no reply. This reads like a proof... but I noticed you started with "I think...". Mind if I ask how sure are you? Also the mention of "corners" puzzled me a bit. I assume you mean the face pieces which point toward the corners. Since they don't have assigned possitions on each faces (like the face centers on a 4x4x4) could two of those be swapped with the last two edges to make a mirror solution possible?

Carl
Sorry for saying "corners"; yes, I meant the face/triangle pieces. I was out of town when I posted earlier today; now that I'm back home and have had a chance to examine the edges of a physical Pyraminx Crystal to double-check what I was visualizing, I am 100% sure.

Showing that it's impossible to solve the edges of a Starminx into a mirror image color scheme (ignoring all other pieces) is equivalent to showing that it's impossible to solve the edges of a cornerless Pyraminx Crystal into a mirror image color scheme, because the edges start the same and move the same. Every face turn of a Pyraminx Crystal or Starminx performs two 5-cycles of edges, so an odd permutation of edges can never be reached from the solved state. If you hold a Pyraminx Crystal with White at the front and Purple on top, and try to re-solve the edges mirroring left<->right:

White/Purple and Yellow/Pink stay put -- no problem.

Orange/Red and Brown/Turquoise need flipping -- no problem.

The other 26 pieces are in 13 pairs that need exchanging -- odd permutation -- can't be done. (White/Blue <-> White/D.Green, White/Brown <-> White/Turquoise, Pink/Brown <-> Pink/Turquoise, Pink/Green <-> Pink/D.Blue, Yellow/Green <-> Yellow/D.Blue, Yellow/Orange <-> Yellow/Red, Purple/Blue <-> Purple/D.Green, Purple/Orange <-> Purple/Red, Blue/Brown <-> D.Green/Turquoise, Blue/Orange <-> D.Green/Red, Green/Brown <-> D.Blue/Turquoise, Green/Orange <-> D.Blue/Red, Blue/Green <-> D.Green/D.Blue)

Solving into a different orientation won't help either, as moving from any puzzle orientation to another is always an even permutation of edges (as each rotation of the whole puzzle around a Pyraminx Crystal face performs six 5-cycles of edges).


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Sun Oct 11, 2009 10:48 am 
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stardust4ever wrote:
While we are on the subject, who will volunteer to build this beast:
Attachment:
Ultimate Dodecahedron.PNG
I think I'll call it the "Ultimate Pentagon Ball" :twisted:

What program is that?

Bumrang :solved: :scrambled: :solved:

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Sun Oct 11, 2009 10:58 am 
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Bumrang wrote:
stardust4ever wrote:
While we are on the subject, who will volunteer to build this beast:
Attachment:
Ultimate Dodecahedron.PNG
I think I'll call it the "Ultimate Pentagon Ball" :twisted:

What program is that?

Bumrang :solved: :scrambled: :solved:


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http://www.jaapsch.net/puzzles/sphere.htm

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Sun Oct 11, 2009 11:43 am 
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So, who ended up winning this puzzle form ebay? why doesn't the winner come out and show it off =(

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Mon Oct 12, 2009 9:12 am 
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Julian wrote:
I am 100% sure.
Thanks again.

Drewseph wrote:
why doesn't the winner come out and show it off =(
Agreed... but do we even know if the winner is a member here?

And any update in version 2 while we are on the topic?

Carl

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Mon Oct 12, 2009 10:41 am 
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wwwmwww wrote:

Drewseph wrote:
why doesn't the winner come out and show it off =(
Agreed... but do we even know if the winner is a member here?

Carl


Yes, he is a well-known member of this forum, and seems to win almost all the interesting puzzle auctions he enters (as I remarked in a comment to NeoDarkHaven in this post). But let us not put too much pressure on him. Maybe his time is better spent building puzzles than taking pictures of his collection.

Oh, and I guess a good way of noticing that you have been spending too much time on ebay, is when your brain automatically starts to associate u***c(xxxx), g***s(xxx), o***m(xxx), b***i(xxx), t***n(xxxx) etc. with their real names. :wink:


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Mon Oct 12, 2009 12:11 pm 
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I have my guess.

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Mon Oct 12, 2009 5:07 pm 
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Julian wrote:
13 pair swaps -- an odd number -- hence impossible. If you tried to solve the Starminx into a mirror image state, the closest you could get is all the centers and corners correct, and all the edges correct but for 2 edges that need to swap places.


Good point -- looks like I must have miscounted in my earlier post. That's a nice property for the Starminx to have.

Incidentally, a (six-color) Dino cube can be solved in two mirror-image ways. I just found a simple 12-move sequence to switch between them.


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Oct 13, 2009 12:40 am 
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I have my guess as well.

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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Tue Oct 13, 2009 3:29 am 
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It is not really difficult to identify the buyer.

But in my opinion it is incumbent upon Aleh to show the internals. He is the constructor and he should have the honour to do this and he has the permission to do this.

If he is missing the one or other picture I think the proud owner will contribute photographs.


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 Post subject: Re: ALEH'S STARMINX (V1).
PostPosted: Wed Oct 14, 2009 1:03 am 
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clauswe wrote:
But in my opinion it is incumbent upon Aleh to show the internals. He is the constructor and he should have the honour to do this and he has the permission to do this.
I don't think honour has anything to do with it. Aleh's design is his, and showing the details of it is his option, but by no means obligation. What does he owe anyone? Is the creation of this awesome puzzle not enough?

The way puzzles have been copied these days I fully support a designer keeping their trade secrets to themselves.

Where designers choose to share, great! But that's up to them.

Dave

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