[cjg]

Or a d6 with the 4, 5 and 6 faces blank. When you roll, if the face isn't blank, that's your number. If it is then flip the die over and subtract that number from 7.

Only uses 6 pips.

[ejddhbrbrrnrn]

Pip position encoding can get that down to 3. One pip on 3 adjacent sides.

Centre pip = 1, Edge = 2, Corner = 3

[quirino]

If we're gonna go that route, you can just put a single pip on a corner and derive all of the other positions from that.