What is the quickest way to get a trapezohedron?

Solution 1:

If you are patient, and don't mind getting really bored... Setup Vanille as your party leader, preferably with the Improved Debuffing weapon, and a whole lot of haste. Pick a fight with the big adamantoise right outside the Eden Palace, immediately summon your Eidelon to take out the legs, then send the eidelon home and spam the Death spell. I usually setup the other two party members as synergists to quickly pickup haste and faith.

Interestingly enough - I killed this guy before I ever walked into the Eden Palace, and he never crashed through the glass, it let me loot both treasure spheres located right there!

Some more tips for this technique can be found online.