I've had a lot of people on the internet asking for this, and a lot of people saying it's impossible. Silly people. It's perfectly possible. I'll show you.
Step 1: Cast on one stitch onto a Double Pointed Needle.
Step 2: K1, P1, K1 in the same stitch.
Step 3: Turn the needle and Purl across the row
Step 4: Turn the needle again, Kfb all stitches.
Step 5: Turn the needle and Purl across the row.
Step 6: Turn the needle, Kfb all stitches.
At this point, you should have twelve stitches and something like this:
Step 3: Turn the needle and Purl across the row
Step 4: Turn the needle again, Kfb all stitches.
Step 5: Turn the needle and Purl across the row.
Step 6: Turn the needle, Kfb all stitches.
At this point, you should have twelve stitches and something like this:
Divide these stitches onto three double pointed needles. Knit all stitches, joining the round.
Step 7: [Kfb, K1] around.
Step 8: K around.
Step 9: Repeat 7 and 8.
Step 10: [Kfb, K2] around.
Step 11: K around.
Step 7: [Kfb, K1] around.
Step 8: K around.
Step 9: Repeat 7 and 8.
Step 10: [Kfb, K2] around.
Step 11: K around.
Repeat this process, increasing by one K stitch per set.
Ex) Next round: *Kfb, K3* Repeat
-K
-*Kfb, K4.* Repeat
-K
Etc, etc.
That's basically it. It's based on the head of Katamari Ichigo and on the teapot bottoms in Interweave's Fiesta Tes Set