Quoting:
My mom says they were called Bic Clicks(think that's how it spelled).  ;D
End Quote

Close.  It was the "Flicker".

I remember because that was what my mother used.  I also had to use it because when I started High School, the first day I was told there was a dress code for guys that included shaving!  When I got home, that was all we had in the house so I had to use it until the end of the week when I got paid.

It was actually not a bad shave, because I did not get any knicks from it.  :)  I still wonder why they can make razors for women that don't knick, but they can't do the same thing for us guys.   lol

I did a little searching, and it was made by the "American Safety Razor Company".  It had 8 blades, and you rotated the inner disk to move to the next blade.  WHen they were all used, you threw it away.

http://www.personna.com/products/flicker.htmhttp://www.geocities.com/safetyrazors/schick/bandraz.htm

Quoting:
;D

Holy Moly!

You are AMAZING!   :)

I was looking on the internet for that 'Flicker' ...not knowing its name for ages.
I was 'googling' ladies plastic round razor...and came up with nothing.

You totally made my day!
End Quote

Shhhhhhh, just don't tell anybody that a GUY was the one to help you find it!

;D

Quoting:
It was actually not a bad shave, because I did not get any knicks from it.  :)  I still wonder why they can make razors for women that don't knick, but they can't do the same thing for us guys.   lol
End Quote

I was going to wait and see if someone else would come forward and admit that.. but now that someone has; I say yeah, no kidding.  Much to my wife's chagrin, I sneak off and use her razor instead of my electric one on occasion.  Unfortunately, she finds out easily enough as I dull her blades with one or two uses.  :)

Quoting:
OK, 80's Friends who live in the States.....let me know if you see any 'Flickers' in dollar stores and drug stores. I will send you a money order or something for them.
I live in Toronto, Canada. No Flickers here  :-/

We have maple syrup, though.  Trade?
End Quote

Well, Personna is still in business, and still makes them.  Try asking your local drug store to carry them.  I am sure the will if you ask.

I saw many places online selling them when I looked for those sites.  Try entering "Flicker Razor" on Google.

Quoting:
I "think" the name of the razor was Daisy and was made by Schick.
End Quote

It's ok....mystery already solved. See above. The razor in question is called 'Flicker'.

:)