Flatland And Three-Dimensional Shapes

Geometry Level 3

In Flatland, all its inhabitants are confined to a single two-dimensional plane (just like we are confined to a single three-dimensional space). When a sphere passes through the plane, a Flatland inhabitant can only see a circle that gradually grows to a maximum size, before it shrinks again and vanish.

On another occasion, a Flatland inhabitant claims that it saw a triangle that gradually grew, then became a hexagon for a while, then turned back to a triangle and shrunk away. What three-dimensional object could have it seen?

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