Bop It! Twist It! .... Pixm It?

You are creating a variation of a Romulan pixmit deck. Each card is an equilateral triangle, with one of the digits 0 through 9 (written in Romulan, of course) at the base of each side of the card. No number appears more than once on each card. Furthermore, every card in the deck is unique, meaning no card can be rotated so that it matches (i.e., can be superimposed on) any other card.

What is the greatest number of cards your pixmit deck can have?

There are $\binom{10}{3} = 120$ different combinations of three distinct digits from $0$ to $9$. There are two distinct ways (up to rotation of the equilateral triangle) to order these three distinct digits. (We can see this by say labeling the sides in ascending order either clockwise or counter-clockwise.) This gives a total of $240$ distinct pixmit cards.

If doubles were allowed in the pixmit mix(mit), then there would be $90$ distinct ways to select the combinations ($10$ options for the doubled digit, $9$ options for the additional digit). In this case, all labelings are rotations of one another. You could through in another $10$ distinct cards if triples are allowed, which would bring the total up to $340$ unique pixmit cards if doubles and triples are allowed.