The form name “Triquatrain” was most likely contrived by Robert L. Huntsman as found listed on shadowpoetry.com. However he most likely stole the credit by giving a name to simple didactic verse.
This is obvious because “Jack and Jill” was written in the 1760s.
There is also reference to it in William Shakespeare's A Midsummer Night's Dream at the end of act three: “Jack shall have Jill; Nought shall go ill.” (Just a little history there)
It is a quatrain poem in tri-rhyme with a specific rhyming pattern (see below).
Lines 1 and 3 have internal rhyme whereas lines 2 and 4 do not.
Fred Meets Trixie
Now Fred was nice; he worked in vice
and could not be corrupt.
Take the money, have a honey.
He made them all shut-up.
He closed down rooms that reeked of fumes,
that turned out to be meth.
He smashed their tools, then told the fools,
"Wages of sin are death."
Prostitution? His solution:
Arrest each whore and John.
So straight he played, that I'm afraid.
Some councilmen are gone.
Some lovely chicks had turned some dicks,
(Detectives), I should say.
But, no cutie or real beauty
Could cause our Fred to sway.
Business was down all over town,
confession booths were slow.
The internet was busy yet
it brought no local dough.
Then just by chance one day Fred glanced
across the cafe floor.
As Trixie came (the perfect dame)
right through the joint's front door.
Passions promised in some fashion
many times thru the years,
It seems absurd without a word
said, she had meshed his gears!
After they talked, together walked,
She put him to the test.
"Play on my range," she said," for change
is as good as arrest."