Domino

The excluded domino is number 0 and 0

After listing and cross-referencing all dominoes present in the image against the 28 unique tiles in a standard double-six set, the [6, 6] (double-six) is found to be missing. The set contains 0-0, 0-1, 0-2, 0-3, 0-4, 0-5, 0-6, 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-2, 2-3, 2-4, 2-5, 2-6, 3-3, 3-4, 3-5, 3-6, 4-4, 4-5, 4-6, 5-5, and 5-6, leaving 6-6 as the only excluded tile.

After systematically examining all 27 dominoes in the image and cross-referencing against the complete standard double-six set of 28 tiles (containing all unique pairs from 0-6), the domino [2, 4] is the only tile that is missing from the set.

After systematically cataloging all 27 visible dominoes and comparing against the full 28-tile standard set, the domino [0,3] (blank|three) is the one not present in the image.

After identifying and listing the 27 visible tiles in the image and comparing them to the full double-six set, the only pair not present is 2 and 4.

By counting the occurrences of each number across all halves in the 27 dominoes, each number from 0 to 6 should appear 8 times in a full set. Number 2 appears 7 times and number 6 appears 7 times, while all others appear 8 times, indicating the missing domino is [2, 6].

After systematically examining all 27 dominoes in the image and comparing against the standard 28-tile double-six set, I identified dominoes [0,0], [0,1], [0,2], [0,3], [0,4], and [0,5] are all present. However, there is no domino with the combination [0,6] (blank/zero paired with six dots) visible in any of the positions. All other pip combinations involving 6 are accounted for: [6,6], [1,6], [2,6], [3,6], [4,6], and [5,6] can all be identified in the image, leaving [0,6] as the single missing tile.