My gauge for both the brim (G hook) and shell network pattern (J hook) were tighter than given in pattern, yet the hat fits a bit on the loose side. And I don’t have a small head. With the G hook - 19 st to 4” and with the J hook - just over 2” to 1 shell network pattern.

I worked as written except I began with foundation single crochet instead of chain. The 6 rows gave me 1 1/2”, then 13 rows of shells for another 8”.

1st photo is from the outside (as you work it)
2nd is the inside along with the balance of the yarn from that skein
3rd shows the top of the hat

It can easily be reversible and I rather like the look of the back side of the single crochets.

Pattern is well written and easily understood. There is no chart.