Fig. S2.

Shape change-driven FCC$\leftrightarrow$BCC reconfiguration is accompanied by a first-order thermodynamic phase transition in spheric triangle invariant hard polyhedra. (A) Shapes used in umbrella sampling calculation. (B) Second neighbor-averaged $l=4$ spherical harmonic order parameter ${\overline{Q}}_4$ distinguishes BCC, FCC, and HCP crystal phases in thermal systems of spheric triangle invariant polyhedra. (C) Below the transition (${\alpha }_c<{\alpha }_c^{\ast }$), a metastable FCC free energy basin develops below ${\alpha }_c=0.185$. (D) Above the transition (${\alpha }_c>{\alpha }_c^{\ast }$), the FCC free energy basin becomes dominant above (${\alpha }_c=0.190$). Well above the transition (${\alpha }_c=0.215$), the BCC free energy basin becomes unstable, but there is a second metastable HCP basin.