怎样理解each a roof of poles and arrowweed

For protection from the summer sun, the Mojave lived in open-sided, flat-topped dwellings known as shades, each a roof of poles and arrowweed supported by posts set in a rectangle.

1. each a roof of poles and arrowweed
2. each a roof of poles and arrowweed that are being
3. with each being a roof of poles and arrowweed
4. with roofs of poles and arrowweed to be
5. with roofs of poles and arrowweed that are

不理解答案A里each的作用。我选了E, 但是than are好像也不对。请指教

是独立主格的一种形式：

each型独立主格：(复数名词结尾,each+单数名词(短语)/介词短语/adj短语/-ed/-ing)，用于强调句尾名词