Is there or could there be a city at the centre of Earths core?

Why could I not see all that I feel now..

(*we build tunnels & underground houses, bomb shelters ... so?)

I have little confidence that there could be a city at the center of Earths core because the material that exists there (as far as we know) is inhospitable to life as we know it.  Not only life, but the properties that make up buildings would vaporize due to the temperature at Earths core.  Earths core is comprised of.. *this is the part where I did my research on the subject and found that the question is far deeper than I realized.  I has previously felt that Earths core was molten, and was liquid.  This is not the case.  This is what my research has yielded..

The Earth's inner core is the Earth's innermost part and according to seismological studies, it has been believed to be primarily a solid ball with a radius of about 1220 kilometers, or 768 miles (about 70% of the Moon's radius). It is composed of an iron–nickel alloy and some light elements. 

Therefore, it appears possible that cities could dwell at the center of Earths core.  The material that surrounds Earths core is of high temperatures and is molten.  However, the inner core, being Iron nickel alloy, could in theory house a city. 

Such a magnificent question, from the one who has changed me... forever.  I Love You.