Crystal Clear

Geometry Level 3

The jewelry shop sells its products cut from the same cubic block in 3 different shapes: a triangular-based prism, a square-based pyramid, and an octahedron. The prism has the base area equal to half the area of the cube's base while the octahedron has its 6 vertices on the centers of the cube's faces, and all 3 shapes have the same height as shown in the picture.

Which of these choices would give you more crystal?

I. A full triangular prism or
II. A pyramid plus an octahedron


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