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This was quick, if true.
How does Wolfram Alpha knows that? And since when?
http://hi.gher.space/wiki/Hydrochoron
Those guys should update, and also should Wikipedia.
I don't know how Wolfram Alpha knows; I'm fearfully ignorant of this sort of thing myself. Perhaps there's a well-known decomposition of the 600-cell into nice simple bits whose 4-volume is easy to calculate?