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A vertical plane is any plane where the normal (a line at 90 degrees to the plane) is horizontal. All your walls are vertical planes.

The normal to the plane of the Earth's orbit is often used to define "up" and "down" for planet Earth.

The Earth's axis is tilted at about 23.5 degrees away from this "vertical" line.

Also you could define "vertical" as simply the direction shown by a plumb line.

That's the definition which has walls as vertical planes.

With either definition there will be more than one plane that is a vertical plane.

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