The predominant phase of calcium sulfoaluminate cement, Ca-4(Al6O12)SO4, was investigated using high-pressure synchrotron X-ray diffraction from ambient pressure to 4.75GPa. A critical review of the crystal structure of Ca-4(Al6O12)SO4 is presented. Rietveld refinements showed the orthorhombic crystal structure to best match the observed peak intensities and positions for pure Ca-4(Al6O12)SO4. The compressibility of Ca-4(Al6O12)SO4 was studied using cubic, orthorhombic, and tetragonal crystal structures due to the lack of consensus on the actual space group, and all three models provided similar results of 69(6)GPa. With its divalent cage ions, the bulk modulus of Ca-4(Al6O12)SO4 is higher than other sodalites with monovalent cage ions, such as Na-8(AlSiO4)(6)Cl-2 or Na-8(AlSiO4)(6)(OH)(2)H2O. Likewise, comparing this study to previous ones shows the lattice compressibility of aluminate sodalites decreases with increasing size of the caged ions. Ca-4(Al6O12)SO4 is more compressible than other cement clinker phases such as tricalcium aluminate and less compressible than hydrated cement phases such as ettringite and hemicarboaluminate.