An Alexandrine is a type of poem that is a single verse that contains twelve syllables. This poem is made up of two half verses that contain six words each. The verses are separated by what is called a caesura or a natural pause. The verses can rhyme but they do not have to. When the verses do rhyme the poem does sound better but still rhyming is not mandatory when writing an Alexandrine.
The Alexandrine is a traditional French style poem. It is the French equivalent to the Haiku. This type of poem was the first type of poetry that was written in France. It is possible to use a longer phrase in this type of poetry. The sentences have to have four verses each with six syllables. That will give the poem a total of 24 syllables. The poem should be on the same topic and there will still be a natural pause between the lines.
Alexandrine poetry consists of a line of 12 syllables with major stresses on the 6th syllable and on the last syllable, and one secondary accent in each half line. Originally a twelve syllable meter in French prosody. However, the English equivalent is the iambic hexameter - see meter. An example of alexandrine verse is Testament of Beauty by Robert Bridges.