Can I use the Shining Trapezohedron against Epic Monsters to attempt to move them?
The exact text on the card is: 




  Action: Choose 1 Monster on any space and role 1 die. On a 5 or 6, discard that Monster. On a 1-4, move that Monster to your space.


From the reference guide (page 6):


  Epic Monsters are treated like Monsters for all effects except as described here:
  
  
  An Epic Monster cannot be defeated by any effect except losing Health equal to or greater than it's toughness.
  An Epic Monster cannot be discarded.
  An Epic Monster cannot be moved, except by an effect on its 
  token or the component that spawned it.
  Epic Monsters are never placed in the Monster cup.
  When an Epic Monster is defeated, it is returned to the game box.
  “Monster” refers to a Monster and/or an Epic Monsters. “Non-Epic Monster” refers to a Monster but not an Epic Monster.
  


So no, the Shining Trapezohedron can not move the Epic Monster