28. A rectangular prism with integer centimeter edge lengths has all 6 of its faces painted red, and then it is completely cut into small cubes with edge lengths of 1 centimeter. Among these small cubes, there are 24 cubes with exactly 1 face painted red, and 28 cubes with exactly 2 faces painted red. The original volume of the rectangular prism is $\qquad$ cubic centimeters.
【Analysis】Let the original rectangular prism's length, width, and height be $a, b, c$ respectively.
Since there are small cubes with one face painted, we have $a \geq 2, b \geq 2, c \geq 2$
The number of small cubes with one face painted is $2 \times[(a-2)(b-2)+(b-2)(c-2)+(a-2)(c-2)]=24$
The number of small cubes with two faces painted is $4 \times[(a-2)+(b-2)+(c-2)]=28$
Therefore, $(a-2)+(b-2)+(c-2)=7$,
$(a-2)(b-2)+(b-2)(c-2)+(a-2)(c-2)=12$
Thus, $(a-2),(b-2),(c-2)$ should be $0, 3, 4$ respectively,
i.e., $(a, b, c)=(2,5,6)$
Therefore, the original volume of the rectangular prism is 60 cubic centimeters.