Question

Should the shape of an object be considered a property of the material?

Answer 1

No
For example a rock was broken into one big and one little piece. The properties of these 2 pieces are still the same even though they have different shapes.

Answer 2

No. The shape of an object cannot be considered a property
of the material.

At your party, you might have a turtle carved out of ice. 
At another party, they might have a swan carved out of ice.

Neither swaniness nor turtleness is a property of ice.