Triangular Dominoes

In his patent, Richards used a three-digit notation, referring to the pips in clockwise order from the side(s) with the lowest value.

, there are 76 unique combinations; the reduced set of 35 and 56 in Triangular Dominoes, for 0–4 and 0–5 pips, respectively, result from the additional restriction for increasing values around each side of the tiles when counting clockwise.

This can be demonstrated by examination of the "singles" tiles: where 012 is a valid sequence in Triangular Dominoes, 021 is not, and so the mirror image of each "singles" pattern is excluded; there are ten excluded patterns for the set of 0–4 pips and twenty for the set of 0–5 pips.

By examination, mirror images of the triples and doubles are identical to the original tiles and so these patterns already adhere to the counting-up restriction.

These restrictions and resulting tile set of Triangular Dominoes were retained, with markings moved to the corners using Arabic numerals for Triominoes, which was published in 1965.

[1] This variant is similar to "points", except the matching criterion is the sum of pips on adjacent sides must be a multiple of five.

Corner-to-corner plays are allowed when the player is able to match the number on both sides of the corner.

Alternatively, if the 233 and 133 tiles are laid next to each other, the total sum is 15, divisible by five, and the player is awarded 15 points.