Dominoes spots from one to six are generally arranged as they are on six-sided dice, but because blank ends having no spots are used, seven faces are possible, allowing 28 unique pieces in a double-six set. However, this is a relatively small number especially when playing with more than four people, so many domino sets are "extended" by introducing ends with greater numbers of spots, which increases the number of unique combinations of ends and thus of pieces. Each progressively larger set increases the maximum number of pips on an end by three, so the common extended sets are double-nine, double-12,
Schläfli double six the Schläfli double six is written 1230. As Schläfli showed, the double six may be constructed from any five lines "a", "a", "a", "a", "a", that are all intersected by a common line "b", but are otherwise in general position (in particular, each two lines "a" and "a" should be skew, and no four of the lines "a" should lie on a common ruled surface). For each of the five lines "a", the complementary set of four out of the five lines has two quadrisecants: "b" and a second line "b". The five lines "b", "b", "b", "b", and "b"