I normally open a dataspace with H5Dget_space, then use the
H5Sget_simple_extent_ndims and H5Sget_simple_extent_dims to get the
dimensionality and dimensions..

This example 
http://www.hdfgroup.org/ftp/HDF5/examples/examples-by-api/hdf5-examples/1_8/C/H5D/h5ex_d_unlimadd.c
illustrates this.

I think you can also use H5Dget_storage_size directly if you don't
care about the array structure (or if it's 1D) and just want to dump
the data.

-John

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