Is it possible to get the specific side of a part?

I'm creating a program where you need to know which side of the part is clicked, to determine the orientation of an object that will be attached to the part. The rest I can take care of, but I'm not sure how to get the exact side of the part (i.e, TopSurface, RightSurface, LeftSurface, etc - but with position).

The code itself should print the side of the part that was clicked with the user's mouse, but I have no idea how I'd go about doing this. Here is how I planned on it looking:

local PlayerService = game:GetService'Players'
local Player = PlayerService.LocalPlayer
local Mouse = Player:GetMouse()

Mouse.Button1Down:connect(function()
	local Target = Mouse.Target

	if Target and Target:IsA("BasePart") then
		local MousePos = Mouse.Hit.p
		local PartSide -- Where it calculates the side of the part that's clicked

		print(PartSide) -- Print the position, string, or anything that represents the side of the part that was clicked.
	end
end)

If anyone has any insight on how I could go about solving this, it'd be much appreciated!