<image>As shown in the image, there is a regular octagonal prism with a base edge length of $$3cm$$ and a height of $$6cm$$.
$$(1)$$ How many faces does this prism have in total? Calculate its lateral surface area.
$$(2)$$ How many edges does this prism have in total?
$$(3)$$ How many vertices does this prism have in total?