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1985 AIME Question 15

AIME · 1985 AIME

Question 15

Three $12\text{ cm}\times12\text{ cm}$ squares are each cut into two pieces $A$ and $B,$ as shown in the first figure below, by joining the midpoints of two adjacent sides. These six pieces are then attached to a regular hexagon, as shown in the second figure, so as to fold into a polyhedron. What is the volume (in $\text{cm}^3$) of this polyhedron?

Question illustration