I didnt look this up in the NEC, I advise you to CONSULT WITH LOCAL AUTHORITY OR YOUR UTILITY PROVIDER AND PROFESSIONAL ELECTRICIANS AND ENGINEERS (versus lay Billy Bob and Bubba untrained opinions or my rusty opinion) however here are my thoughts as I best recall... NO WARRANTY
1) First thing is you have to compute the load and overcurrent protection devices and know if your wires ampacity is sufficient.
2) Next, if your enclosing that triplex in conduit (I have no heartburn with that but see my final safety disclaimer) ascertain its ampacity in that environment, because its often used in free air and the more common known and advertised ampacity is for free air NOT enclosed. i.e. it may be rated say 100 amps in free air but less if its enclosed.
3) Is it copper or aluminum?? If aluminum use connectors and lugs and terminations rated for such and any necessary anti oxidant coating
4) FINALLY as we have preached on here for years, is this for a main panel or a sub panel fed by a circuit breaker in your homes main panel, and is it 120/240 volt????
If its 120/240 volt and its a sub panel fed by a breaker in your main panel YOU NEED 4 NOT THREE (Triplex) CONDUCTORS. Two UngrounDED Hots L1 & L2,,,,,,One Grounded Neutral Conductor,,,,,,,One Equipment GroundING Conductor
As always, I'm sure I missed something and hope the electricians and engineers can add to this as needed and correct any errors, I'm never too old to learn I figure.
Sorry to give you a complicated answer, but that just the way I'm wired and experienced and trained.
SHORT ANSWER sure run triplex in conduit provided its ampacity is properly computed and sufficiemnt and you may or may not have enough conductors???? See the above.
FINAL CAUTION AND DISCLAIMER
Ive seen triplex in free air and buried mostly as a service feed from utility transformer to the residence, but NOT familiar with its use indoors I HAVE NO IDEA IF SUCH IS PERMISSIBLE OR NOT and I'm too busy and lazy to look it up lol SURE Billy Bob and Bubba it will "work". Its your home and life and safety and money and decision, not mine, do as you wish.