The angular design was so that guns were in place to sweep attackers from every wall. That is, some of the guns are able, without having to be moved, to fire close to and parallel to every wall.
No attacker would be able to rush the wall and remain there in relative safety (given the benefit of covering fire) and set to work breaching the wall.
Note the "Plan of Johnston Fort at Cape Fear", where the angle of the top left point seems to be inaccurate, such that the covering cannon at the base of the upper right point can't quite shoot along the wall of the upper left point.
Also note the Bristol Ferry Fort, with it's not-quite-star design, can't quite protect the small sides of the points, given the angles of the gun ports (if accurate.)
Also it seems interesting that the designer of the Ontario Fort has put heavier walls toward Lake Ontario, where ship cannon may be used by an attacker. It was the opposite case in Pittsburgh, where one would expect the main attack by land.
In France, many forts has been build by a military engineer named Vauban[1] in the 17th century. His life is highly impressive. He worked a lot on fortifications and breaking of sieges. Outside of military building, he has been a scientist and an economist with modern views on taxes.
I highly recommend to visit Hôtel des Invalides war museum in Paris. It´s worth the time just to admire the collection of (huge) scale models of the fortified cities in the France of the S XVIII. They are impressive and show how the cities used to be. They are originals from the time, perfectly conserved, they were originally created to better appreciate the capabilities of a fortification.
There are a ton of great napoleonic fortifications in the rhineland. A couple years ago I was touring through and stopped for an afternoon wandering around Neuf Brisach. Didnt realize it was one of his last projects.
There is a common misconception that cannons rendered tall walls useless because they could easily distroy them. Rather guns benefited less when shooting from tall walls than arrows reducing ther advantage. Plus defensively they protected less of the inner structure as cannon could fire on taller archs and still be effective. So, it came down to a simple cost benifit analysis and ditches are fairly cheap to construct vs. the extra thick walls needed vs cannon.
Not as beautiful, but the fortifications at Rhodes are unbelievably impressive and after 1481 were built to withstand cannon barrage. The Knights of St. John had unbelievable financial resources available to them and the fortress was state of the art at the time and have the distinction of never having been defeated in battle. Despite being attacked several times by very large, very determined forces.
The story of how Rhodes eventually fell to the Ottomans is even more proof at what an astonishing fortress the place is [1] - the walls never fell.
The siege [2], (the second major attempt) which took from June to December of 1522, with nearly quarter million men assaulting, and only 7,500 defending, ended only when both sides were too exhausted to fight any further. The Ottomans had lost half their forces during the siege, and the Knights of St. John had dwindled down to about 1,500, but still defending. Exhausted the Ottoman forces (under Suleiman the Magnificent) offered a deal. Leave in peace, taking what wealth you can, and you'll be granted safe passage off of the island. After some back and forth, the Knights took the offer and eventually ended up in Malta where they started over again (and engaged in yet another round of incredible impenetrable fortress building).
When the Ottomans took control, they patched up the damage they did and maintained it basically as-is for 400 years.
Walking around the fortress is like receiving a master class in fortress engineering and design. It's hard to understand exactly how a fortress like this could repel so many until you walk up to some of the approaches and start counting how many cannons could shoot at you simultaneously in crossfire. Trying to enter away from a main approach (like over a wall) meant climbing up and down several layers of very tall walls [3], essentially forcing you to trap yourself in a canyon where more clean lines of fire were aimed at you. It's not just high walls, it's interlocking pieces that slow, route and line up attackers to be slaughtered by the tens of thousands.
The fortress presented an unsolvable puzzle no attacker could overcome.
From the tail end of these, Fort Jefferson down off the tip of Florida is a fabulous example. The largest masonry structure in the United States. 16 million bricks, a hexagon about 150 meters on a side. It pretty much takes up an entire island.
These are not nearly the most impressive examples of this kind of fortification; as North America was a relatively peripheral area in the 18th century, only relatively small and cheap versions of star forts were built there.
Another example: "The Castle" in Cape Town, South Africa is actually a fort built between 1666 and 1679 by the Dutch East India Company and has the same five-pointed structure.
And is a national monument, as it is the oldest existing colonial building in the country.
I'll add another example; La Mola in Menorca [1], built by the English starting in 1708. I was going to post a google map link but strangely it is a censured zone. I guess it still has other uses besides tourism.
Is still a military zone, but has no strategic use now a days.
It´s just a museum, were you can visit the old fortress and a coastal artillery battery from the beginning of sXX that used the only Vickers 385/45 remaining from the times of the first world war (huge cannons that were also mounted on Battleships).
La Mola didn´t see action, and in fact it just became obsolete just before being finished (it never got the cannons) because new rifled canons with longer range made close fire and old fortress design completely infective (The bunker and underground fortification era began).
I thing it´s more impressive the fortress that it´s at the other side of the bay, la fortaleza de San Felipe, demolished by the Spanish government once menorca passed again to Spanish control because it was so big that they were unable to man it.
http://descobreixmenorca.com/wp-content/uploads/2014/03/dmen...
Hmm, it's not the one I'd pick. I cycled through Rocroi a couple of years ago, it's much more impressive from the air than it is on the ground - you're mainly looking at earthworks, and can't really see the plan. I passed through Verdun the next day, it's similarly disappointing - you can't see it until you're close by, then it's just a wall. Vauban fortifications with the advantage of high ground are far more photogenic on foot, eg Belfort and Briançon.
Some of these star forts survived into the present day: Fort Monroe[1] was decommissioned in 2011. It's a real shame that it was, but c'est la vie (or, in this case, c'est la guerre).
For a rather asymmetric alternative Gibraltar is a fascinating visit. The tunnels are amazing, they're still rediscovering parts, not surprising given there are more miles of tunnel in the Rock than there are miles of road on the surface.
No attacker would be able to rush the wall and remain there in relative safety (given the benefit of covering fire) and set to work breaching the wall.
Note the "Plan of Johnston Fort at Cape Fear", where the angle of the top left point seems to be inaccurate, such that the covering cannon at the base of the upper right point can't quite shoot along the wall of the upper left point.
Also note the Bristol Ferry Fort, with it's not-quite-star design, can't quite protect the small sides of the points, given the angles of the gun ports (if accurate.)
See http://en.wikipedia.org/wiki/Star_fort
Also it seems interesting that the designer of the Ontario Fort has put heavier walls toward Lake Ontario, where ship cannon may be used by an attacker. It was the opposite case in Pittsburgh, where one would expect the main attack by land.