How to sharpen eyeliner

[Baldieheid]

I bought a couple of eyeliner pencils online, and they're plastic, but they don't twist up. I must have to sharpen them somehow....do I need a special type of sharpener as my usual one just won't trim the plastic. What on earth do I do?

Which ones are they?

It's the Rodial smokey eye pen. Which is a pencil. Very soft and lovely re the liner, but the pencil part is horrible - it's plastic and my sharpener is not doing the job.
I don't understand why they'd do that....

It's described as 'easily sharpened with a makeup sharpener' maybe you just need a new one?

Yes, probably. I've ordered a new one, my blade is probably blunt. I wonder why they don't just use wood though.

Oh certainly, horrible bits of shaved off plastic.
You might as well use it up now you have it though.

Yep, just won't buy it again.