The type of poem structured with three lines and a specific syllable count is a Haiku.
A Haiku is a traditional form of Japanese poetry that consists of three lines. The syllable pattern for a Haiku is 5-7-5, meaning the first line has 5 syllables, the second line has 7 syllables, and the third line has 5 syllables.
Here is an example of a Haiku:
Autumn leaves falling (5 syllables)
Whispers in the gentle breeze (7 syllables)
Nature's quiet song (5 syllables)
In contrast, a Limerick is a five-line poem with a specific rhyme scheme, a Sonnet is a 14-line poem with a specific structure, and a Narrative is a poem that tells a story.