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In sage 9.2+ (and probably since a while), you can use the optional package pynormaliz to do parallel volume computations. If you have sage compiled with

MAKE='make -j64'

one a computer with 64 processors you should use that many processors (I hope at least, it worked for me for 8).

The following used 8 threads for me:

sage: P = polytopes.cyclic_polytope(10,20, backend='normaliz')   # optional - pynormaliz
sage: P.volume()  # optional pynormaliz
904076817914638457425434331054080000000