Please restore the 5 by 5 grid containing 10 ternary numbers with no leading zeroes.
The crossword-like definitions follow:


Across:
I. a cube
II. twice a permutable (in base 10) prime
III. divisible by eleven
IV. the number of trees with 10 vertices
V. a square

Down:
1. repdigit in base 12
2. a factorion in base 10
3. a semiprime
4. a square of a prime
5. its cube in base 10 uses only 3 distinct digits

Rem: I have built it bottoms-up. Hope there is only one solution...