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Is a basement always a story?

The print is too small to see clearly, but it looks like basement to first floor is 11 ft something. The basement isn't a "story above grade plane" as long as it's under 12 ft., and the first floor is less than 6 ft. above grade plane. It looks OK to me.
 
Picking up on what steveray says about a space that has no habitable or usable space not being a basement - I am inclined to agree.
To put it another way, try this thought experiment:
If a "basement" is any portion of a building below grade, then is the section drawing below showing any of the following:
1. A basement?
2. A building with two stories?
3. A one story building with an additional story below grade plane?​




upload_2019-10-28_14-21-17.png
 
If the space is to be unuseable then why is it an issue?
If the perimeter does not extend beyond the property lines why wouldn't that then limit its size?
What purpose would be served if it is unuseable?
 
To be considered a story a basement will need an occupiable space/use which means it has to meet the minimum ceiling height requirements IMHO

1208.2 Minimum ceiling heights.
Occupiable spaces, habitable spaces and corridors shall have a ceiling height of not less than 7 feet 6 inches (2286 mm). Bathrooms, toilet rooms, kitchens, storage rooms and laundry rooms shall be permitted to have a ceiling height of not less than 7 feet (2134 mm).
 
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