I have a vector of numbers which is generated from a normal distribution with sd=x1 and mean=0. When I'm turning these numbers into absolute values, I suppose that the they will follow half-normal distribution with the same sd.

My question is, if I initially start at having a vector of absolute values which generated from half-normal distribution, would it be mathematically sound to add the negative values of these numbers and then find the combined standard deviation between absolute values and negative values to recreate the normal distribution?