Hydrogen-bonded assembly of multiple components into well-defined icosahedral capsules akin to virus capsids has been elusive. In parallel, constructing robust zeolitic-like cluster-based supramolecular frameworks (CSFs) without any coordination covalent bonding linkages remains challenging. Herein, we report a cluster-based pseudoicosahedral H-bonded capsule Cu, which is buckled by the self-organization of judiciously designed constituent copper clusters and anions. The spontaneous formation of the icosahedron in the solid state takes advantage of 48 charge-assisted CH···F hydrogen bonds between cationic clusters and anions (PF), and is highly sensitive to the surface protective ligands on the clusters with minor structural modification inhibiting its formation. Most excitingly, an extended three-periodic robust zeolitic-like CSF, is constructed by edge-sharing the resultant icosahedrons. The perpendicular channels of the CSF feature unusual 3D orthogonal double-helical patterns. The CSF material not only keeps its single-crystal character in the desolvated phase, but also exhibits excellent chemical and thermal stabilities as well as long-lived phosphorescence emission.