Clouds composed of CO2 ice form throughout the Martian atmosphere. In the mesosphere, CO2 ice clouds are thought to form via heterogeneous ice nucleation on nanoparticles of meteoric origin at temperatures often below 100 K. Lower altitude CO2 ice clouds in the wintertime polar regions form up to around 145 K and lead to the build-up of the polar ice caps. However, the crystal structure and related fundamental properties of CO2 ice under Martian conditions are poorly characterised. Here we present X-ray diffraction (XRD) measurements of CO2 ice, grown via deposition from the vapour phase under temperature and pressure conditions analogous to the Martian mesosphere. A crystalline cubic structure was determined, consistent with the low-pressure polymorph (CO2-I, space group Pa-3 (No. 205)). CO2 deposited at temperatures of 80-130 K and pressures of 0.01-1 mbar was consistent with dry ice and previous literature measurements, thus removing the possibility of a more complicated phase diagram for CO2 in this region. At 80 K, a lattice parameter of 5.578 ± 0.002 Å, cell volume of 173.554 ± 0.19 Å3 and density of 1.684 ± 0.002 g cm-3 was determined. Using these measurements, we determined the thermal expansion of CO2 across 80-130 K that allowed for a fit of CO2 ice density measurements across a larger temperature range (80-195 K) when combined with literature data (CO2 density = 1.72391 - 2.53 × 10-4T - 2.87 × 10-6 T2). Temperature-dependent CO2 density values are used to estimate sedimentation velocities and heterogeneous ice nucleation rates, showing an increase in nucleation rate of up to a factor of 1000 when compared to commonly used literature values. This temperature-dependent equation of state is therefore suggested for use in future studies of Martian mesospheric CO2 clouds. Finally, we discuss the possible shapes of crystals of CO2 ice in the Martian atmosphere and show that a range of shapes including cubes and octahedra as well as a combination of the two in the form of cubo-octahedra are likely.