We can think of the #"HgI"_3^"-"# as being formed by the reaction
#"Hg"^"2+" + 3"I"^"-" → "HgI"_3^"-"#
The electron configuration of a neutral #"Hg"# atom is
#"Hg"^0 = "[Xe] 6s"^2 "4f"^14 "5d"^10#
For #"Hg"^"2+"#, the electron configuration is
#"Hg"^"2+" = "[Xe] 4f"^14 "5d"^10#
The #"Hg"^"2+"# ion, however, has vacant #"6s"# and #"6p"# orbitals.
It can hybridize a #"6s"# and two of the #"6p"# orbitals to form three new vacant #"sp"^3# hybrid orbitals.
These can each overlap with a filled #"5p"# orbital of an iodide ion.
Thus, the new ion is trigonal planar, and the #"Hg-I"# bonds are coordinate covalent bonds in which the iodide ions are contributing both electrons of the covalent bond.
