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The two types of designs for Roman ceilings were primarily vaulted or divided by beams. Roman architecture is renowned for its innovative approaches to structure and design, particularly in the use of the arch and vault. The vaulted ceilings allowed for expansive and open spaces that were decorative and functional. These structures made use of arches to distribute weight, enabling larger interior areas compared to flat ceilings, which were more limiting in size and flexibility.

Divided by beams refers to the structural approach where beams were used to create sections within a ceiling. This design not only supported the overhead structure but also added visual interest and complexity to the ceiling design, incorporating different materials, colors, or finishes. This combination of vaulted ceilings and beams was essential for both aesthetic appeal and structural integrity in Roman buildings.

While the other options mention various types of ceiling designs, they do not specifically highlight the main characteristics of Roman ceilings as accurately as vaulted or divided by beams, which were integral to their architectural style.