Even at extragalactic distances, the shape of supernova ejecta can be effectively diagnosed by spectropolarimetry. We present results for 17 type Ia supernovae that allow a statistical study of the correlation among the geometric structures and other observable parameters of type Ia supernovae. These observations suggest that type Ia supernova ejecta typically consist of a smooth, central, iron-rich core and an outer layer with chemical asymmetries. The degree of this peripheral asphericity is correlated with the light-curve decline rate of type Ia supernovae. These results lend strong support to delayed-detonation models of type Ia supernovae.