A histogram is a graphical representation of data that uses rectangular bars to represent the frequency or relative frequency of different intervals or categories. The description provided in the question includes the following characteristics:

I. Rectangular bars of equal width: Each bar in the histogram has the same width, which ensures consistency and accuracy in representing the data.

II. The height of each rectangular bar is proportional to the frequency of the corresponding class interval: The height of each bar reflects the frequency or relative frequency of the data it represents. This helps visually convey the distribution of the data.

III. Rectangular bars have common sides with no gaps in between: The bars in a histogram are drawn adjacent to each other without any gaps, creating a continuous visual representation of the data.

Based on the description, all three characteristics (I, II, and III) are necessary to fully define a histogram.