Excluding volume, what do the objects that sank have in common?

Answer is: objects that sank have in common: buoyancy and density.

Objects that sank are negatively buoyant. Buoyancy or upthrust is an upward force exerted by a fluid that opposes the weight of an object.

Density is defined as the mass of an object per unit volume. In the case of water, an object with a density more than 1 g/cm³ (density of water) will sink.