That's an Ikea faucet, right? I had to do the same thing a couple of days ago. I ended up dremeling (drilling, effectively) two holes in what was left of the aerator, as far apart from each other as I could, and twisted the thing out with some round nose pliers pointing upwards. The top of the aerator is much more solid than the brittle honeycomb below it. I am now waiting for an adapter piece from China that will allow me to screw on a different type of aerator, externally, so to speak, so this can't happen again.
Plumbing
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I'm not familiar with that particular model but with most faucets around here the whole chrome piece can be unscrewed.

Can you put some putty up the faucet, let it dry a little then try turning the glob of putty... Or, try chewing gum.


