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A heptagon has seven sides, a hexagon six, a nonagon nine, and an octagon eight. So in 5 heptagons, 2 hexagons, 4 nonagons, and 3 octagons there are (5*7)+(2*6)+(4*9)+(3*8) = 35 + 12 + 36 + 24 = 107 sides altogether.

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