Is the Red Army hat a three-cornered hat or an octagonal hat?

It’s an octagonal hat.

The octagonal hat and the red five-star are the symbols of the Red Army and one of the most conspicuous parts of the Red Army's military uniforms.

The Red Army’s octagonal hat was a gift from Feng Yuxiang. Feng Yuxiang failed and resigned during the Central Plains War that broke out in 1930, and his troops were absorbed by Chiang Kai-shek. Feng Yuxiang was forced to go abroad for "investigation". Before leaving, he quietly donated all the hundreds of thousands of military uniforms he originally planned to revive to the Red Army. Since then, the Red Army has had its own military uniform, which is the Red Army uniform with the octagonal hat as its symbol.

Historical origin:

The gray octagonal hat became a special symbol of the Red Army. It is said that once the Red Army ambushed the White Army. When it gets dark, the Red Army disperses into ditches and hillsides to capture prisoners and mingle with the enemy. It's dark and you can't see people clearly, so how can you capture prisoners.

The only identifiable mark is the difference between the enemy's military cap and the Red Army's: the enemy's military cap has a short and hard brim, while the Red Army's octagonal hat has a long brim, is made of soft cloth, and has a A strip of bamboo strips was propped up. Therefore, when Red Army soldiers met someone, they would often hug him at the waist. If they felt that the other person had a hard cloth hat with a short brim, they would hand over his gun.

Reference for the above content: Baidu Encyclopedia - Octagonal Hat