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the word part omo means - Feedz API

📅 May 17, 2026 👤 scraface

May 17, 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) $:

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

📌 Given integer coordinates and regular triangular face, $ (0,0,0) $ is a valid answer.

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