The LG 360 camera fits perfectly into the hole of my bicycle helmet, no mounts needed, just stick it from the inside through the hole and it gets stuck, will not go anywhere 
Footage is ok, not too much helmet in the picture, I am completely covered under the helmet, camera does not stick out too much above my head so it draws less attention than cycling with a monopod. I can easily press the on/off button. Disadvantage: very difficult to connect it to a powerbank with a USB cable. Maybe the insta360 One is better, it has a USB connection to the side, maybe it will fit too (the hole is oval shaped, measures 24mm x 50 mm), @tankaru?