Since the page is inaccessible right now, here's the tl;dr (though it's not long at all): The UK's new £1 coin has 12 sides. That makes it impossible for it to

Since the page is inaccessible right now, here's the tl;dr (though it's not long at all): The UK's new £1 coin has 12 sides. That makes it impossible for it to be (like the 7-sided 50p and 20p coins) a shape of constant diameter, which might make it roll less well and make things harder for the makers of vending machines. When OP heard that the new coin was going to be 12-sided, he wrote to the Royal Mint. When the final design came out, it turned out that they'd taken this objection into account but found that a 12-sided coin with curved sides and rounded corners rolls well enough. Very good, but OP would have been happier with an odd number of sides. The end. (Is the constant-diameter property actually relevant to vending machines? It seems to me that unless you're trying to fit the coin down a "tunnel" of absolutely minimal size, what matters is how close it is to constant radius -- i.e., how nearly circular -- and constant diameter is a red herring.)