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To determine this, start by drawing the Lewis structure. When you do so, you’ll see that the central carbon atom has 4 bonding regions. Using VSEPR, this molecule would have a tetrahedral shape. Even though tetrahedral is a symmetrical molecular shape, drawing out the dipole moments (from partial positive C atom to partial negative I atoms) shows that the dipoles do not cancel, thus making CH2I2 polar.
I believe that this molecule would be nonpolar since carbon, hydrogen, and iodine all have very similar electronegativities. Carbon and iodine have electronegativites of 2.5 and hydrogen has an electronegativity of 2.1. There isn't substantial enough electronegativity difference between atoms to result in a polar molecule.
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