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Home » Gallade’s Hidden Flaw: The Secret That Scores Big Fans Off Guard! - inBeat

Gallade’s Hidden Flaw: The Secret That Scores Big Fans Off Guard! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A science communicator creates a video showing symmetries in polyhedra using a regular icosahedron centered at the origin. If three vertices of this icosahedron are located at $ (1,1,0) $, $ (1,0,1) $, and $ (0,1,1) $, and all coordinates are integers, find the coordinates of one other vertex that forms a regular triangular face, consistent with icosahedral symmetry.

📌 Solution: In a regular icosahedron, all edges are of equal length. First, compute the distance between the given points:

📌 Distance between $ (1,1,0) $ and $ (1,0,1) $:

📌 Similarly, distance between $ (1,0,1) $ and $ (0,1,1) $:

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