A Spider-Fly Problem with a Surprising Solution

A spider and a fly are on opposite walls of a 30 × 12 × 12 meter room. The spider is 1 meter above the floor, the fly is 1 meter below the ceiling. They are both 6 meters from adjacent walls, as shown in the diagram below.

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If the fly does not move, what is the shortest distance the spider can crawl to reach it? (along the surface only — no web-shooting!)