The tetractys, made famous by Pythagoras, has become a modern poetry form. Ten was thought to be a number of power, and by having the lines leading up to the last line equal ten, it seemed logical for the creator of the tetractys poetry form to name it such.
A tetractys has in total, five lines. The syllables are as follows:
First Line - 1 syllable
Second Line - 2 syllables
Third Line - 3 syllables
Fourth Line - 4 syllables
Fifth Line - 10 syllables
In any formatting, it gives a triangle shape. It can be reversed, starting with the ten lines, and moving downwards for a "reversed tetractys." There are also what is called "double tetractys" in which two you have a tetractys followed immediately by a second tetractys. A normal tetractys followed by a reversed tetractys would give you a diamond shape.
There is no set rhyme scheme for a tetractys, you can choose to rhyme or not. Here are two examples from Ray Stebbing, who credits himself with coming up with this form: