Puzzle 12: Two paper cubes

Puzzle 12: A man has two paper cubes on his desk. Every day he arranges both cubes so that the front faces show the current day of the month. What numbers are required on the faces of the cubes to allow this for all possible days in the calendar?
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Solution:

Dice 1: 012678

Dice 2: 012345

Note: we use 6,9 by inversion of them by 180 degrees.