Q: Why do stairways that are enclosed on both sides require a handrail?

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That would be a polygon

ay shape that is enclosed and doesn't have any curved sides

Yes. A polygon is by definition a shape enclosed by multiple sides - the smallest number of sides that enclose an area is three.

There are quadrilaterals that have no parallel sides. (basically, a quadrilateral is just any enclosed shape with 4 sides) But all quadrilaterals have angles.

A polygon hasthree or more straight sides (and no sides which are not straight);the same number of vertices;an enclosed plane area.

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It can, if that is the design your require

According to the building code, handrails are required on both sides of a stair, except for in individual dwelling units, stairways less than 44" wide and stairs having less than four risers. This means you need a handrail on at least one side of any stair more than just a single riser. (This is in addition to the requirement for guardrails if there is a dropoff to the side of the stair.) In a single-family home, DIY setting, you may be able to get away with less, but it would probably be unsafe. I think you will be fine if it is two foot or less that's the code for G.a

It is a carport that has a garagedoor in the front and is enclosed on all sides by metal bars.

the garden was enclosed on all sides by a fence.

A polygon is a 2-dimensional area that is enclosed by straight lines. These straight lines are its sides.

Any shape that is enclosed and has three sides is a triangle.

It is a plane area enclosed by three straight sides.

That would be a polygon

It is any plane shape which is enclosed by 12 straight sides.

ay shape that is enclosed and doesn't have any curved sides

Yes. A polygon is by definition a shape enclosed by multiple sides - the smallest number of sides that enclose an area is three.

They are not homogons. because there are two qualifications for a polygon: it is enclosed and it has straight sides. that's just the way things are