Once you have one Trapezohedron, you can turn that one into three.

To do this, pick up a Mistilteinn, one of Vanille's weapons, buyable from
Plautus's Workshop for 11,000 gil. Along with this, you will need the
following materials:

159 Sturdy Bone \
89 Superconductor \ Total gil:
2 Particle Accelerator / 1,507,400 gil
28 Ultracompact Reactor /

1 Scarletite - (bought for 100,000 gil from "The Motherlode", or farmed
from enemies. See "Obtaining Catalysts" section.)
1 Trapezohedron


Now, use the following items to upgrade the Mistilteinn in this exact
order (for best cost effectiveness)

36 x Sturdy Bone
50 x Superconductor

1 x Scarletite

36 x Sturdy Bone
2 x Ultracompact Reactor
15 x Sturdy Bone
27 x Superconductor

1 x Trapezohedron

36 x Sturdy Bone
26 x Ultracompact Reactor
36 x Sturdy Bone
2 x Particle Accelerator
12 x Superconductor


The weapon should now be a maxed out Nirvana. Once you dismantle this, you
will receive:

71 x Monstrous Fang
60 x Entrancing Tail
36 x Moonblossom Seed
10 x Tear of Woe
3 x Trapezohedron

Taken from Gamefaqs =] Hope this helps.