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Simply put, why can't you draw square planar molecules top down (so you don't have to use depth bonds)?

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You can do that. For example, a Google Image search for "cisplatin structure" suggests that although the hashed + wedged depiction is more common, the four plain bonds depiction is also in regular use.

For more detail on what's "acceptable" or not, refer to: Graphical representation of stereochemical configuration (IUPAC Recommendations 2006). Pure Appl. Chem. 2006, 78 (10), 1897–1970, DOI: 10.1351/pac200678101897. They recommend the hashed + wedged depiction, but do not prohibit four plain bonds (section ST-2.6, pp 1942–3). There is some rationale for this, which may go some way towards explaining why the hashed/wedged depiction is more common: it explicitly differentiates the square planar structure from other tetrahedral centres in organic structures.

The first recommended depiction should be drawn with two solid wedged bonds and two hashed wedged bonds. The two solid wedged bonds should be positioned below the central atom, while the two hashed wedged bonds should be positioned above. [...] It is also acceptable to draw similar structures with plain bonds. There are some cases where this drawing style would even be preferred, particularly when all four bonds are required to be in the plane of the paper by virtue of other aspects of the structural diagram [...] The similar depiction with the bonds themselves positioned along the axes is acceptable but should be avoided as it is extremely commonly used to represent tetrahedral centers, either if the tetrahedral configuration is nonstereogenic (carbon tetrachloride) or in Fischer projections. enter image description here enter image description here

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