Dugu Xin's Seal
Dugu Xin's, an official seal used during the Northern and Southern Dynasties period in China, has the form of a rhombicuboctahedron with eight triangular and eighteen square faces. If all of its vertices are on the surface of a cube with edge length , find its edge length.
Resource: Gaokao 2019
The answer is 0.414214.
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1 solution
The diagram below shows a top-down view of the seal in its unit cube-shaped box
(for clarity, the square and triangular faces are in different colours.) If x is the edge-length of the seal, we have 2 x + x + 2 x = 1 . Solving this gives x = 2 − 1 ≈ 0 . 4 1 4 … .