What's the trick to looking beautiful without any sleep?

Become a vampire. :)

Without a doubt, some nice stylish mirror sunglasses :)

Hang out with blind people.

My looks fade considerably with every hour of sleep I miss.

I don't worry about such things. Maybe that's why I sleep better. ;)

Black lights.

Good genes and under-eye concealer.

maybe some more makeup

Sorry I need my beauty sleep. 

Cool shades

Don't ever show them what you look like with sleep.  That way they will have nothing to compare. 
Also, make sure your teeth are brushed and minty fresh every hour.  People attach the smell of fresh breath to mornings and starting a new day.  They will think you already slept.
If you can, take a shower or a bath.  It will make you feel more awake.  If you can't at least splash water on your face. 
Change your makeup
Iron your clothes.
Now that I've written all these hints, by the time you are done doing them you could have slept a wink or two! Giggles!
Walk with a smile and your good to go.
Oh, deodorant helps too! ;) This post was edited by Merlin at July 13, 2017 7:20 PM MDT

Surrounding yourself with really ugly people who don't get any sleep. This post was edited by LyricalOne at July 10, 2017 12:57 PM MDT

Die and get mummified and beautified by a very good undertaker.

"Become a Harem Girl."

Makeup. Lots and lots of makeup.