Isotropic minerals are those which belong to the isometric
These minerals have three mutually perpendicular crystallographic axes, all of equal length. This causes the light to encounter the exact same atomic environment no matter which direction it travels through the mineral, which unlike in anisotropic minerals, means the light travels at the same velocity in every direction through the mineral.
Viewing Isotropic Minerals with a Petrographic/Polarizing Microscope:
When light travels at the same velocity in each direction, there is no birefringence, so the minerals stays extinct (black) upon rotation under cross polarized light. This is because under crossed polars, all unchanged light is blocked out, and isotropic minerals allow the light to propagate through with out change. This is an identifying characteristic of isotropic (and therefore isometric) minerals. However, there are some angles at which anisotropic minerals can be cut that will cause them to display this behaviour, so many crystal orientations must be observed.
When viewed under plane polarized light, an isotropic mineral will display even relief upon rotation (meaning its outlines look the same no matter the orientation), since its refractive index (how it bends light) is the same in every direction. Again, anisotropic minerals oriented in specific ways can display this behaviour.
Since total extinction is observed, no interference figure can be obtained from an isotropic mineral.