Does a triple divorce take effect on a wife who swore not to wear the niqab, and then her husband swore an oath of triple divorce upon her to wear it, but she did not wear it within the period intended by the husband? Is it permissible to extend the period, and does the divorce take effect in this case?

As long as you intended a specific duration in your oath and your wife did not continue to wear the niqab thereafter, you have broken your oath. This is because an oath is based on the intention of the one who swears it, and your intention was only for that period, so it does not extend beyond it. "The basis of an oath is the intention of the one who swears it. If he intends by his oath something that it can bear, his oath is directed towards it, whether what he intended is consistent with the apparent meaning of the wording or contrary to it."