Please help, thanks!

You’re looking for a plane which divides a closed brep into two portions with the exact same volume?

I think the answer is yes. What I want to create is a ice-ray pattern in 3d. In the 2d version, a straight line with random angle is drawn from the center of the shape to split it into identical shapes, I think that rule still applies on the 3d version which means the cut plane always passes through the center point of the volume. Any idea?

It’s called the ham-sandwich theorem, there’s infinitely many ways to slice a volume into two equal volumes using a flat plane, but unless the shape is one of a small group of special ones, no straightforward way to find it in one go.