Fig. S6.

Shape change-driven FCC$\leftrightarrow$BCC reconfiguration is accompanied by a first-order thermodynamic phase transition in spheric triangle invariant hard polyhedral shown here with both BCC (solid lines) and FCC (dashed lines) initialization. Differences between curves indicate systematic errors in computing the location of the transition but that the thermodynamic nature of the transition is robust. (A) Free energy curves of hard polyhedra as in Fig. S2. (B) Free energy curves of hard polyhedra as in Fig. S3 (gaps in red dotted lines indicate insufficient statistics in one umbrella sampling window). (C) Free energy curves of hard polyhedra as in Fig. S4. (D) Free energy curves of hard polyhedra as in Fig. 2.