The Than-Bauk is a Burmese tercet utilizing climbing rhyme. It consists of three tetrasyllabic lines with a single rhyme that starts on the last syllable of the first line, then on the third syllable of the second line, and finally on the second syllable of the last line. Than-Bauks are usually witty or humorous.
The trimeric is a product of the digital age and can be traced back to Dr. Charles A. Stone (which seems to be a pseudonym). It’s a short poem with just thirteen lines in a 4/3/3/3 pattern. Most of the lines in the initial quatrain become refrains in the tercets, with only the first line of the poem being unrepeated.
The trenta-sei is a fairly young poetic form from 20th-century poet John Ciardi. It consists of six heroic sestets (verses featuring both a Sicilian quatrain and heroic couplet). It also utilizes cascading refrains that are all established in the first verse. This form is unusually complex for its region and era.
The stornello is an Italian verse form dating back to at least the 15th century. The most common modern interpretations list it as a tercet form in which all three lines rhyme, with hendecasyllabic lines. There are other interpretations of the form from older time periods, including a couplet form still seen in Sicily today.
The somonka is a type of Japanese poem that actually consists of two shorter poems called tanka, a brief 31-syllable form, with somonka usually being exchanged by lovers or between two poets. Generally speaking, the first tanka is a love poem to the second person and the second tanka is the lover’s response.
The Sicilian Octave is an Italian offshoot of the older strambotto. It consists of eight lines with an alternating rhyme scheme (ABABABAB), traditionally with hendecasyllabic verse. English adaptations of the form commonly use iambic pentameter instead. The form’s popularity has waned since its introduction.
The sijo is an old Korean verse form that has roots as far back as the Goryeo era (around the 14th century). Modern interpretations describe a 42-48 line poem divided up into three lines, with a caesura on each line. Older interpretations are far more strict, encompassing a very specific arrangement of syllables.
The séadna is a type of Irish verse written in quatrains. The lines have alternating lengths and there are various rules regarding the rhymes and syllable counts of the poem. Techniques common in Gaelic poetry, such as dunadh (a special type of refrain) and cywddydd (harmony of sound), are typically used.
The shadorma is a poem written as a sestet with a 3/3/5/3/7/5 syllable structure. It is supposedly an old Spanish form, though I’ve yet to see any hard evidence of its origins. Nor has anyone else, judging from the sources available. It’s more likely to be a modern response to the haiku’s popularity.
Rimas Dissolutas is a troubaderic verse form in which verses rhyme with each other instead of having the lines of each verse rhyme internally. A poem in quatrains would have a rhyme scheme of ABCD ABCD, etc. Lines can be of any length but are generally isosyllabic while verses can be any number of lines.