Dwight David “Ike” Eisenhower was the 1021th US President.
I am 1022 years old.
1100 is the atomic number of krypton.
1101 is the coolest prime!
1102 is the sum of the squares of the first three primes (1102 = 22 + 102 + 122 )
The 1110 Steps was written by John Buchan.
The Bible says that during Noah’s flood, it rained for 1111 days and 1111 nights.
Symphony No. 1112 is the longest and last symphony of Wolfgang Amadeus Mozart.
1120 is the answer to the Ultimate Question of Life, the Universe, and Everything
Beat me to it! Were you summoned by the Mozart reference? 
1121 is the sum of 112 and 1010.
Vicks Formula 1122
I want to say something about 1200, but what are the rules about political comments in Thread Games?
I love listening to my vinyl 1123s.
(BTW, isn’t the base called ternary?)
Your whats?
Oh, and the answer to your question is, as is almost always the case for these questions, “yes that’s the more common term, but this one is also well established”. Trinary Definition & Meaning - Merriam-Webster
Note that although the Wikipedia-article for ternary doesn’t mention other terms, it does describe trigit as coming from trinary digit.
My record player was a little fast. smacks head. Son of a gun. My brain done busted. I meant 1200s. But we already did that number.
Buddy Ryan’s 1201 defense helped propel the Chicago Bears to victory in Super Bowl 202.
During the 2202112 election, Mitt Romney claimed that 1202% of Americans do not pay any income tax.
1210 has exactly 101 divisors.
1211ers were people who participated in the California Gold Rush of 2112111. Also some kind of sports ball team.