One would think that it would be easy to find data on emerald cut 
emeralds, but Web searches yields almost entirely emerald cut 
*diamonds*.  I have to specifically exclude the word "diamond" from the 
search in order for the Web to acknowledge that any other gems exist on 
this planet other than diamonds.

But even so, it seems impossible to find information on cut angles for 
emerald.  Lots of descriptions of the emerald cut, but no actual 
numbers.  I did find one informal recommendation for an emerald cut--for 
sapphire!  But sapphire's IOR is considerably higher than emerald's.

So, I tried finding some viable angles myself.  I'm not having any luck; 
all but the shallowest crowns leak light like a sieve:

   emerald_specs-flat.png
     Demonstrates the range of pavilion angles that contain the light
     with a flat crown.
   emerald_specs-near_flat.png
     Any crowns steeper than this will leak light.
   emerald_specs-shallow.png
     A damn shallow crown.
   emerald_specs-steep.png
     And it doesn't get any better at steeper angles.

I used an IOR of 1.584, which is what I estimate is emerald's IOR at a 
green wavelength, based on 1.580 at D and a dispersion of 1.089.

I went searching deeper, and found a cut designed by Jim Perkins, and 
published in Lapidary Journal Jewelry Artist, October 2010.  Although 
his cut is not a traditional step cut, I tested his angles in my rig:

   emerald_specs-perkins-long.png
     The angles Perkins used on the long side of his cut.

It still leaks, even though he calibrated his cut for an IOR of 1.54, 
which I imagine less forgiving than emerald's.  Is it possible to get a 
leakless emerald cut with a decent crown?  Or do they count on leaked 
light being reflected back from the setting?  Will light coming into the 
crown at an angle leak less, or at least compensate?  (I suppose I can 
find out if I budget more render time.)  Can someone channel Steve Paget?

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