Torus lab — the flat torus that presents as a sphere

A genus-1 body: gold outer sheet reads as a planet; the cyan tunnel wall runs pole-to-pole through the interior. The white loop is one unbroken poloidal wrap. Drag to orbit, scroll deep to fly in through a mouth. The slider blends in the first Nash–Kuiper corrugation octaves (heights exaggerated; slopes are the invariant).