Instead of splitting, you can scale the box by its center point by 0.5, then move the scaled box in the 8 vector directions from the center to each of the original vertices, scaling the vectors by 0.5.
Instead of splitting, you can scale the box by its center point by 0.5, then move the scaled box in the 8 vector directions from the center to each of the original vertices, scaling the vectors by 0.5.