Final answer:
The Colosseum's arena compartments, specifically the underground staging area known as the hypogeum, were not meant to be visible to the public. Other features such as the arena floor, marble seats, and numbered gateways were all designed to be seen and to enhance the spectator experience.
Step-by-step explanation:
The feature of the Colosseum that was not meant to be visible to the public is arena compartments. These underground areas were known as the hypogeum and were used for staging and preparing participants and animals for the spectacles, such as gladiator battles and animal fights, that took place on the arena floor above. The other options listed, such as the arena floor, marble seats, and numbered gateways, were all meant to be visible as they contributed to the organization and the splendid appearance of the venue, enhancing the experience for the spectators.
The numbered gateways, for example, were comparable to a modern stadium, helping the spectators find their assigned seats efficiently. The Colosseum was designed not only for these practical purposes but also to impress both the people of the Roman Empire and those they wished to dominate with its architectural grandeur. Thus, while the hypogeum was crucial to the operations of the Colosseum, it was kept out of sight to maintain the illusion and spectacle above.