Imperial Amethyst

You can learn the patterns to cut this gem through different ways :

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Once a day, you can learn a pattern, the cheapest way, spending 3 uncut gems of the color you want.

The gem pattern learned has the same color as the gem you just spend. If you already know all the patterns of this color, an other random MoP-rare gem pattern is taught to you.

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• Blue : 4 different gems.
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• Red : 5 different gems.
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• Yellow : 5 different gems.
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• Orange : 22 different gems.
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• Purple : 14 different gems.
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• Green : 18 different gems.
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• total = 68
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You can also spend Spirit of Harmony 3 by 3, without cd, to learn an random MoP-rare gem pattern at any time.

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• Secrets of the Stone
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Open a Jewelcrafting panel first!
Use this command line to print how many MoP-rare patterns you've learned of each colors. (only works enGB/enUS)
Open a Jewelcrafting panel first!
/run local c,r,w,z=0,0,{"Riv","Primo","Sun'","Verm","Impe","Wild"},{0,0,0,0,0,0} for i=1,3^7 do local s=GetTradeSkillInfo(i) or 1 for j=1,6 do if strfind(s,"%s"..w[j]) then r=r+1 z[j]=z[j]+1 end end end print(r.."/68") for i=1,6 do print(z,w) end

MoP rare gems:

Red - Primordial Ruby
Orange - Vermilion Onyx
Yellow - Sun's Radiance
Green - Wild Jade
Blue - River's Heart
Purple - Imperial Amethyst

MoP uncommon gems:

Red - Pandarian Garnet
Orange - Tiger Opal
Yellow - Sunstone
Green - Alexandrite
Blue - Lapis Lazuli
Purple - Roguestone

Pandarian Garnet and Tiger Opal seem to have their icons the wrong way round.

Note to those with [skill=755] who are searching for some information as I was about obtaining rare, MoP gems:

When [spell=31252], the best ore to receive rare, Mist of Pandaria gems is either Black Trillium Ore OR White Trillium Ore, with an average, gem, drop rate of 17% each (according to Wowhead).

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This ore can be obtained directly via two methods:
      1) These can be mined from two, rare-node-spawns: [object=209313] or [object=209330].
      2) If you are Revered with [faction=1272], plant [item=85215] for random chances at obtaining either type of Trillium Ore per plant.

This ore can be obtained indirectly by executing two steps:
      1) If you are Revered with [faction=1272], plant [item=89233] to farm Mote of Harmony (yields 1 Mote per plant) and eventually make Spirit of Harmony to use as
          currency in the next step.
      2) Purchase a stack of 5 Trillium Ore in exchange for 1 Spirit of Harmony.

Here is a quick list of each rare gem for easy-viewing:
Primordial Ruby
Vermilion Onyx
Sun's Radiance
Wild Jade
River's Heart
Imperial Amethyst

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Since Trillium nodes are rare spawns, a more surefire way to obtain rare, MoP gems is through [skill=171], specifically through Transmutations.
Being a Transmutation Master will result in the highest transmutation yields. Here is a quick list of each transmutation recipe for easy-viewing.

NOTE: Each recipe requires a Golden Lotus and the Uncommon version (listed below) of each, rare gem.

Tiger Opal
Lapis Lazuli
Sunstone
Roguestone
Pandarian Garnet
Alexandrite

Transmute: Primordial Ruby
Transmute: Imperial Amethyst
Transmute: Sun's Radiance
Transmute: Vermilion Onyx
Transmute: River's Heart
Transmute: Wild Jade

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If you DO decide to transmute and you are hard-up for Golden Lotus, you can:

      A) buy 2 in exchange for 1 Spirit of Harmony from NPCS:
            [npc=66685] (horde)
            [npc=66678] (alliance)

      B) become Revered with [faction=1272] to purchase, then plant:
            [item=85216] to get a rare chance at gathering a Golden Lotus
            [item=89233] to farm Mote of Harmony (yields 1 Mote per plant) and eventually make Spirit of Harmony to use as currency in option "A".

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LASTLY,

The least-effective way to farm rare, MoP gems is through prospecting:
Kyparite OR Ghost Iron Ore
Each having roughly a 5% rare-gem, drop rate (according to Wowhead).

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I hope this was helpful and saved you some time! Please feel free to add or suggest anything else!