While you might hear that the gogyohka is a short Japanese poem form and mistakenly conflate it with the extremely popular haiku, the two are not related. The gogyohka is a modern invention of the Japanese poet Enta Kusakabe (born 1938) and only has two simple rules. It is five lines long. Each line is one phrase.
The mondo is a Japanese poetic form emerging from Zen student-master traditions. The poem ultimately consists of two verses, with one posing a question and the other answering, usually in 5-7-7 syllable structures.
The imayo is a poem form from 12th century Japan that was originally intended for song. It has since been adapted into a poem with four 12-syllable lines, each divided up into sections of seven and five syllables by a caesura. Despite its similarities to the haiku, the imayo is rarely mentioned in the western world.