Seventy-eight is the sum of the numbers from 1 to 12, which makes it the twelfth triangular number. That single fact accounts for its appearance in several places that look unrelated.
Triangular numbers count the ways of choosing two things from a set. Choosing two from thirteen gives seventy-eight, and this is why Metatron's Cube has seventy-eight lines: the figure is constructed by joining each of the thirteen circle-centres of the Fruit of Life to every other, and thirteen points taken two at a time give seventy-eight connections. No line is selected and none omitted, which is what makes the construction determinate. Because the thirteen centres lie on a regular triangular lattice, many of those lines overlap visually, so a drawing shows far fewer than seventy-eight distinct strokes, seventy-eight is a fact about the points, not a count of marks on the page.
The same reasoning gives seventy-eight as the number of distinct pairs in any group of thirteen, and as the number of tiles in a double-eleven domino set.
Seventy-eight is also 2 x 3 x 13, with eight divisors. It has no other distinguished arithmetic properties, and it is worth saying so, because the coincidence of the tarot count with the triangular number is exactly the kind of thing that attracts unjustified interpretation. The tarot has seventy-eight cards because twenty-two trumps were added to a fifty-six card game pack. That the total happens to be triangular is a coincidence, and no fifteenth-century source shows the least awareness of it.