We use DEM simulations to analyze the microstructure and bulk modulus of dense frictionless agglomerates composed of platelets of increasing platyness. We show that the solid fraction increases from that of a packing of spherical particles as the platyness increases, but declines again beyond a peak value. The coordination number follows the same trend whereas the contact coordination number remains nearly constant and equal to its isostatic value of 12 when three single contacts are attributed to each face-face contact and two single contacts to each face-edge contact. We show that the evolution of the microstructure is echoed by the bulk elastic modulus, which considerably increases with platyness.