The Star Compass is a light blue transparent orb with patterns on its surface. It has a structure inside of it and a metal ring around it.
Riko illegally took it back to the orphanage with her as her own personal item instead of turning it in for money. The needle inside it always points downwards, no matter how much you turn and shake it. Riko claims it points to the bottom of the Abyss.
Riko took it on her journey, but quickly lost it on the 1st layer when she got excited and it slipped out of her hand while she was shaking it. It hasn't been seen since.
Vueko inherited one from her caretaker, and then used it to traverse the sea to find the Abyss with Ganja. She gave it to the island natives in an exchange. Whether Riko's compass is the same one as Vueko's is unknown.
Riko's theory that it points to the bottom is backed up by the fact that while in the hands of Vueko, it always pointed towards the Abyss; even when she was far away from it.