The Azadi Barracks are the second major feature of Tower Square besides the Tower. As the Barracks are not yet complete the Azadi army camps in tents spread over the Square. It appears to already be in at least partial use, however, as one of the soldiers invites April back to spend the night there with him and some friends.
The Hagia Sophia in Istanbul (Robert Raderschatt).
Construction of the Barracks and the Tower continues apace simultaneously, and the two are to be connected by a bridge leading from the balcony outside the Emissary's office to a minaret on the Barracks. Indeed, the scaffolding under this bridge is how April gains access to the balcony in order to eavesdrop on the conversation between the Emissary and the Prophet.
The Barracks are fairly typical of the Islamo-Persian architecture exhibited by the Azadi, although it is made of brown stone rather than the more dominant white. Its inspiration appears to be the real-world Hagia Sophia, which is itself a Byzantine basilica later converted into a mosque after the fall of Constantinople in 1453: the main change being the addition of four minarets.