Distinct band gaps and isotropy combined in icosahedral band gap materials
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The icosahedral tiling modulo the unit cell of the PAS results in point sets circumscribed by triacontahedra on a fcc lattice (a). The QPNC consisting of steel beads in polyester (b). Shapes of the (pseudo) zone boundaries of the fcc (c) and the icosahedral (d) structures. Experimental longitudinal wave transmission spectra of the QPNC along a twofold axis (solid line) and its APNC for the  direction (dashed line) (e). Calculated band structure of the APNC along the  direction (f). Transmission (dashed line) and reflection (dotted line) spectra for shear waves for the APNC (g) and QPNC (h) [directions as in (e)]. The shaded regions in (e)–(g) denote the frequency ranges of the longitudinal hybridization and the shear Bragg gaps.
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