This quite simple stole/shawl/wrap is indeed reversible-- a cascade of lace arrows set against a background of purl, then knit stitches. The whole is knit on needles ostensibly a little too large for the yarn's weight, but that just serves to accentuate the eyelet pattern and give more drape to the piece. Various ways of wearing it are shown here, but there are many more; arranging it around your head, you have an elaborate scarf or simple treatment in addition to having it serve as a scarf. Very versatile, and something you'll need year-round, unless you live on the Equator.
