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The square is between the post office and the bank. There is no obvious symbolism of these buildings. Mr. Graves is the postmaster and therefore linked to the post office; his name "Graves" is symbolic of the ritual sacrifice that is the lottery but even this is a stretch in connecting his name to the post office building. But, the square itself is symbolic because it is the center of town. This is the place where all rituals occur:
The lottery was conducted--as were the square dances, the teenage club, the Halloween program--by Mr. Summers, who had time and energy to devote to civic activities.
Knowing this, the townspeople treat the lottery like any other tradition, like any other ritual. This is the same place they have dances and meetings. This further underscores the consequences of blindly adhering to traditional rituals. Clearly, the lottery is useless, while the other social functions have a useful purpose.
The black box which holds the names is also a square (or rectangle). Supposing any more symbolism than the comparison of the square to the black box is up to the interpretation of the reader or critic. One such interpretation is that squares have specific dimensions: four sides, four corners, and four angles of exactly ninety degrees each. There is no way to deviate from these dimensions and still be a square. This is the same attitude the villagers have towards tradition. They feel (with the notable exception of Mr. Adams) that they just can not deviate from tradition, even though the lottery seems like a pointless exercise of violence and cruelty.
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