We report the discovery of a new binary icosahedral phase in a Sc-Zn alloy obtained through solution-growth, producing millimeter-sized, facetted, single grain, quasicrystals that exhibit different growth morphologies, pentagonal dodecahedra and rhombic triacontahedra, under only marginally different growth conditions. These two morphologies manifest different degrees of quasicrystalline order, or phason strain. The discovery of i-Sc$_12$Zn$_88$ suggests that a reexamination of binary phase diagrams at compositions close to crystalline approximant structures may reveal other, new binary quasicrystalline phases.