Start with standard worsted-weight yarn and #7 needles. Use 2 strands, to make it thick. These directions make an octagon approximately 5 inches in diameter.

Directions:

Cast on 10 stitches
Rows 1-10 (approximate) Knit front & back of first stitch, then knit the rest of the row.
Measure to see if your angle is the same width as the bottom. Keep expanding until these measurement are the same.
Rows 11-20 (approximate) Knit until the side measurement is the same as the bottom and angled section.
Rows 21-30 (approximate) Knit 2 together at the beginning of each row until the top angle is the same as the bottom angle and you're back to 10 stitches.
Bind off.

When I finished this mat, I realized how perfect it would be as a potholder, hotpad, or "doily" for under a potted plant. You could make them any size. They'd make nice gifts, made up in sets.

Now back to my project:

I doubled my yarn, threaded it through a tapestry needle, and used a running stitch about a half inch in all the way around, so I could gather it up. The result looks like a granny's nightcap. (If you need one of those for a doll, this pattern could adapt nicely.)

I made a couple of 5 minute flowers for tassles and here is the finished product.

5 Minute Flowers

Using #15 needles, cast on 10 stitches. Leave a long tail (I left about 8")
Knit 3 rows.
Bind off, again leaving a long tail.
Pull the top tail down to the bottom, so it won't stick up in the middle of your flower.
Roll up the flower from end to end. The cast-on row will be the base of the flower. The looser, bound-off edge will be the "petals."
Wrap one of the tails tightly around the base of the flower, then tie it securely to the other tail. Your flowe is finished. I timed this and it really takes only five minutes and less than 3 yards of yarn to make one of these.