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...