Plan for Castle Pendaris

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From the reading in our class I can see there are a number of problems.  The gate needs a barbicon.  The corners need towers, even the rounded corners.  This is a castle built by an invading country deep within the captive country.  The purpose of the castle is to serve as a military stronghold, to house the school for acolytes studying air magic, and to protect the temple (of the air god).