Why were fortresses often built pentagonal?
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It has to do with the angles of the corners as well as the interior space of the fortress. In the gunpowder age fortresses were protected by cannons stationed in what were called bastions. Bastions were so shaped to allow the guns to shoot along the walls of the bastions and between the bastions. The principle was that every inch of the fortress’s wall was covered by guns.
The fewer number of sides to the fortress, the narrower the angle at the salient (tip) of the bastion. This meant it was weaker against enemy gunfire and had less interior space, so the guns could be more crowded and harder to work. Also, there would be less total space inside the fortress itself, so there would be less room for barracks, magazines, storehouses, etc.
On the other hand, the more sides the fortress had the more guns it needed for defense to cover all those walls. So that was a design consideration too.
Smaller earthwork forts were often square, but for a masonry fort five sides (and five bastions) was usually the minimum. The pentagon had a good balance between interior space and number of guns need for defense. A large fortress built around a city would usually have many more sides, sometimes as many as one or two dozen.
Once in a while someone would build a triangular fort but that was very rare. They were just too small and weak.
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