Can't figure out how to disassemble my Eljer faucet...

So grateful to find this forum. My 1/2 bath has Eljer faucets that were installed in 1979 that are gritty and very difficult to turn on and off.

While attempting to disassemble, I have come across a configuration that I am not familiar with. I remove the top cap, then the center screw. Next the clear plastic knobs. After that I am used to seeing a stem or cartridge configuration but on this particular sink all I see is a 4-point large metal star. No place for an allen key or place to loosed with strap wrench or channel locks. Please help. I have photos below.

http://www.flickr.com/photos/drjordansteinberg/4949239662/


http://www.flickr.com/photos/drjordansteinberg/4948650271/


http://www.flickr.com/photos/drjordansteinberg/4948650009/

links working

HI there.

I got my links to work. Sorry for the inconvencience. They were working the first time when I logged off.

PLease help!

its a two part handle the ''4 point metal star'' is part of the handle and is corroded to the stem pull wiggle pull wiggle pull puulll

You may need a handle puller to get that handle adapter off. Soak it with white vinegar to start ( down in the screw hole)

https://terrylove.com/forums/Products/Faucet-Handle-Puller__180.aspx