In general, any polyhedron, subtending a solid angle $\Omega&lt;2\pi$ sr at each of its vertices, is called a convex polyhedron. 

While any polyhedron, subtending a solid angle $\Omega&gt;2\pi$ sr at any of its vertices, is called a concave polyhedron. 

It is very practical that a convex polyhedron has its each vertex elevated (protruding outward) while a concave polyhedron has any of its vertices indented on the surface.      

Instrinsic definition of concave and convex polyhedron
I read a book about American English. It reports that, in standard informal conversations, American English doesn't use the /ɔ/ sound; it uses the /ɑ/ sound and /ʌ/ and /ə/ are not different. Are they really?
That book would not use the /ɔ/ and /ʌ/ sounds, but when I look in my American English Dictionary for some words, such as more, door, and love, they are reported to be pronounced /mɔr/, /dɔr/, and /lʌv/.
How should I pronounce these words, if there are no /ɔ/and /ʌ/ sounds?  Should they be /mɑr/, /dɑr/, and /ləv/?
Can /ɑ/ sound replace /ɔ/, and /ə/ replace /ʌ/ in every word?
What about formal American English? Does it have /ɔ /and /ʌ/ sounds or not?
