Here's the pattern for making this particular snowflake. It's surprisingly simple, you really only need basic crocheting skills to make it. I found this pattern online and printed it out several years ago. I don't think the original pattern is available on the net anymore, so I'll share it here. Just note that this is not my pattern, it's Priscilla Hewitt's! And for lots more gorgeous snowflake patterns, go to Crochet Pattern Central.
Priscilla Hewitt’s Picot Snowflake Ornament
Aus and NZ crocheters bear in mind that 1 US dc = 1 tr, 1 US sc = 1 dc, and so on.
Materials:Small amount crochet cotton and Steel crochet hook [I don’t think it really matters what cotton and hook you use. Just pick whatever cotton you like – I used some medium-fine mercerised white crochet cotton – then find a hook that seems the right size, according to how thick the cotton is and whether you are a tight or a loose crocheter - Editrix]
Pattern Note: There should be an unworked ch between each picot.
To make dc picot: ch 5, dc in the 4th ch from hook
To make cluster picot: ch 5, yo insert hook in the 4th ch from hook and pull up a loop, yo and pull through 2 loops on hook, yo, insert hook in the same ch and pull up a loop, yo and pull through 2 loops on hook, yo and pull through all 3 remaining loops on hook, sl st in the same ch
Work tightly for best results. If you tend to crochet loosely, use a smaller size hook.
Ch 6; join with a sl st in the first chain to form ring
Round 1: Ch 3 to count as the first dc, work 11 more dc in the rings; join with a sl st to the top of the beginning ch 3. (12 dc)
Round 2: Ch 1, sc in the same st as joining, (2 dc, ch 3, 2 dc) in the next dc, *sc in the next dc, (2 dc, ch 3, 2 dc) in the next dc * Repeat from * to * 4 times; join with a sl st to the first sc. (6 “points”)
Round 3:Ch 1, sc in the same st as joining, (dc picot, cluster picot, dc picot), ch 1, sl st in the same sc, ch 1, 2 dc in the next ch-3 sp, work 2 dc picots, work 3 cluster picots, working along the other side, skip 3 cluster picots, sl st in the next unworked ch, (ch 4, dc in the 4th ch from hook, skip next dc picot, sl st in the next unworked ch) 2 times, 2 dc in the same 3-ch sp, she 1 skip next 2 dc, *sc in the next sc, (dc picot, cluster picot, dc picot), ch 1, sl st in the same sc, ch 1, 2 dc in the next ch-3 sp, work 2 dc picots, work 3 cluster picots, working along the other side, skip 3 cluster picots, sl st in the next unworked ch, (ch 4, dc in the 3rd ch from hook, skip next dc picot, sl st in the next unworked ch) 2 times, 2 dc in the same ch-3 sp, ch. 1, skip next 2 dc* Repeat from * to * 4 times; join with a sl st to the first sc. Fasten off. Weave in ends.
You’ll need: Fabric stiffener, small zip lock bag, stainless steel straight pins or wooden toothpicks, waxed paper, sheet of flat Styrofoam, fishing line.
Place snowflake and fabric stiffener in a small plastic zip lock bag. Work stiffener into the snowflake through the closed bag then let it soak for at least one hour. Place a sheet of waxed paper on a flat sheet of Styrofoam. Remove snowflake from bag then wring out any excess stiffener. Shape snowflake on waxed paper paper and tack in place with pins or toothpicks. Allow to dry completely. Remove pins. Add a loop of fishing line to the snowflake to hang.