If NOT all symmetric, unimodal distributions are normal, then please describe a distribution that is symmetric

Question

and unimodal that is not NORMAL. Please cite examples.

Statistics experts are welcomed to answer this question.
By the way, what do you really mean by "NORMAL", statistically?

Answer 1

The distribution of the sum of two rolled dice is symmetric (2 = 12, 3 = 11 etc.) and unimodal (7 is more frequent than any other result), but its shape is not "normal".

The distribution of the sum of N rolled dice is symmetric, and unimodal (at 3.5 * N), and its shape approaches more and more closely to "normal" as N increases.

Answer 2

Equal in all directions