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 Post subject: Best yield on a perfect cube
PostPosted: Sun Mar 24, 2013 1:11 pm 
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Hey all! I was thinking about this a while back, and figured I'd run some of this stuff by you all.

Let's imagine that someone gives you a perfect cube of some kind of synthetic, whatever material you like best. What's the best yield you can get out of this cube? Assume that all the views I'm talking about are as if you have the cube sitting on a table, and you're looking at one of the flat faces, down the a axis.

Well, the beginner thing to do would be to dop to one of the flat faces of the cube, and cut a square design. This loses a lot of material when you cut the pavilion, and loses a lot more when you cut the crown.

The next thought would be to tilt the cube 45*, so now, one of the edges of the cube is a keel. You could grind down one of the edges to make a new flat, dop there, and cut a keeled square design (opposed bar anyone?). This would be a huge boost to yields.

But what would be the next step up? What kind of new orientations can we find for the cube? Let's imagine that now, we're balancing this cube on one of its vertices. We can treat this corner as if it would be our new pavilion. As it turns out, the cross section of this particular view is a TRIANGLE. If we grind down one of the vertices and dop there, we can get a triangle that's already basically preformed for us! This should give similar yields to the keeled design.

...except there's one more step up. Keep the cube balanced on a vertex, but this time, take the cross-section right between the four staggered vertices. This cross-section is a HEXAGON, with all the crown and pavilion angles already preformed at 45*. With a mindful design, it should be possible to get yields in the 60% range or better (I haven't done any booleans yet to actually figure this out, since I haven't written a design for this purpose yet.)



Thoughts?


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Sun Mar 24, 2013 11:55 pm 
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Keeping the cube balanced on a vertice saw it in half and have two preformed pyramids?

Andrew


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 12:02 am 
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akearns wrote:
Keeping the cube balanced on a vertice saw it in half and have two preformed pyramids?

Andrew

You can only do that with an octahedron, not a cube. :( With a cube, you'd get a weird part-pyramid-part-octagon-ish thing. Although I see where you're going with this...


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 3:16 am 
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You'll get a fantastic recovery rate if you leave it as a cube.

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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 9:54 am 
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I think you have to supply more parameters. The obvious answer is leave it as a cube, but I assume that isn't satisfactory.


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 10:35 am 
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Arya Akhavan wrote:
akearns wrote:
Keeping the cube balanced on a vertice saw it in half and have two preformed pyramids?

Andrew

You can only do that with an octahedron, not a cube. :( With a cube, you'd get a weird part-pyramid-part-octagon-ish thing. Although I see where you're going with this...


True, they wouldn't be pyramids, but I'll bet this would still give you best yield in a design with a table.

A lazy option would be to go through your designs (using DataVue? I don't have it...) and find the one with the best Vol/W3 ;)

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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 11:20 am 
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akearns wrote:
Keeping the cube balanced on a vertice saw it in half and have two preformed pyramids?

Andrew


you know smart asses like you really piss me off



especially when they beat me to it!


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 12:03 pm 
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Arya Akhavan wrote:
...except there's one more step up. Keep the cube balanced on a vertex, but this time, take the cross-section right between the four staggered vertices. This cross-section is a HEXAGON, with all the crown and pavilion angles already preformed at 45*. With a mindful design, it should be possible to get yields in the 60% range or better (I haven't done any booleans yet to actually figure this out, since I haven't written a design for this purpose yet.)


I made some pictures. It looks like the best fitting shape in this case would be triangle, not hexagon.
Also, remember that you'll get two medium sized stones, if you only cut one larger stone even with less recovery it can be more valuable than a couple of smaller stones.

Image

For large triangle, hexagon or round:
Image

For large rectangular design:
Image

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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 2:15 pm 
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Hey Egor, thanks for the renderings! For the hexagonal cross section, I wasn't talking about literally cutting the cube in half, but using that hexagon as the girdle outline. If you imagine the stone dopped at a vertex and you cut in to create that hexagonal outline, you should have enough room to do a workable design. Maybe. I have to think about this more.

And yeah, your pictures really make visualization easier! Thanks for doing than :)


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 3:07 pm 
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Yes, now I see your idea!
Looks like it can give a very good yeld for a large hexagon, starting from the picture 2 and making the girdle where the cut plane in the picture 1!

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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 3:20 pm 
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I did it a coupla times (check the "no, it's trigonal" design with an hexagonal outline and a 3-fold pavilion... Oh, it fits so well with a cube dopped along on one of its 3-fold axes! :wink: my first test cut was a cube of YAG...) but the main problem is that the angles for a good light return are different. Maybe with opal/fluorite/etc. it would be better. :D


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Mar 25, 2013 3:40 pm 
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Another thought.

Look at picture 1. Let's assume that the hexagon view is the girdle outline, and the point at the back is the pavilion. Some basic trig and geometry tells me that the angle between the hexagonal plane and the floor is approx. 54.74 degrees. If I'm thinking about this right, that's the same angle as the faceting angle.

So if we try to get it down to 43 (quartz) or something reasonable for YAG/CZ...we'd still lose a decent amount of material. Still, though, it's a hell of a lot better than if we dopped on one of the cubic faces :D

Also Marco, I just took a look at that design! Looks like you already beat me to this idea :mrgreen:


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Apr 01, 2013 9:53 am 
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I have done it with a cube of Topaz, 10 mm cube. Recovery was good although I did waste some of the corners. I'll try to find the post, it was a while ago.

Sean.


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 Post subject: Re: Best yield on a perfect cube
PostPosted: Mon Apr 01, 2013 10:03 am 
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After giving the idea some thought I decided to actually do it and see what the result would be. A step cut would have been best for yield but to be realistic I thought something that cut to a point would be more practical so did a L&S 1.4 design and a step cut with what was left. I thought clear Topaz with a sort of average sg would do, quartz would have been a little lighter and and and well I have plenty of clear Topaz.

Don't mind the cheapie plastic vernier, it's close enough for the job. Not being confident enough to get it centered again after weighing I thought working off the sg would be good enough so 3.52 X 5 = 17.6 carats at start.


Pavillion is done, it was 14.2mm at the widest, then a bit for a girdle line as well as a whoops on P4 which has the same indexing as P3 but different angle had me down to 13.3mm.


with the pavillion done it was time to saw off the bit that was surplus to the crown.


The big bit finished up at 13.3 x 9.5mm and weighs 8.24 carats, so 46.8% recovery.


The little bit ended up at 9.5 x 6.6mm and weighs 2.36 carats, 13,4% recovery, just a simple step cut for that one. Added up the total recovery is 60% so not too bad.
On the finished stones you need to use your imagination and pretent the fluff isn't there, it took as long to get a passable picture as it did to do the project.
The real plus in it for me was finding out how easy it is to post images using imageshack. The first attempt was a false start, anybody know how to remove it?

Enjoy,

Sean


Last edited by Sean Lines on Mon Jul 11, 2011 6:02 pm, edited 1 time in total.

Unfortunately the pictures seem to have disappeared.


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