  We study the antiferromagnetic spin-1/2 Heisenberg model on the highly
frustrated, three-dimensional, hyperkagome lattice of Na_4Ir_3O_8 using a
series expansion method. We propose a valence bond crystal with a 72 site unit
cell as a ground state that supports many, very low lying, singlet excitations.
Low energy spinons and triplons are confined to emergent lower-dimensional
motifs. Here, and for analogous kagome and pyrochlore states, we suggest finite
temperature signatures, including an Ising transition, in the magnetic specific
heat due to a multistep breaking of discrete symmetries.
