Is there any "nice" representation for algebraic numbers of degree 3 (or higher)?

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Every decimal number have a finite decimal expansion !

Every rational number has its decimal expansion becomes periodic after some digits.

Every rational number has a finite continued fraction representation.

Now every algebraic number of degree 2 has a periodic continued fraction representation after some digits.

Is there another representation of numbers such that an algebraic number of degree 3 or more is periodic after some digits?