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The paper determines the vertices and surface volumes of all rounding polytopes for com-monly used rounding methods: the quota method of greatest remainders, and the divisor meth-ods. These methods are used to round continuous non-negative weights summing to one to non-negative integers summing to a predetermined accuracy, e.g. to 100 when rounding to percentages. Our results are of interest when average properties of rounding methods are in-vestigated, and an example from political science is included