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why did gas prices go up yesterday - GetMeFoodie

📅 May 1, 2026 👤 scraface

May 01, 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) $:

🔥 Popular Posts

An astrophysics researcher analyzes stellar motion with vectors $\math...
The area is the magnitude of the cross product $\mathbf{r} \times \mat...
\mathbf{r} \times \mathbf{s} = \begin{vmatrix} \mathbf{i} & \mathbf{j}...
= \mathbf{i}(2 \cdot 4 - (-1) \cdot 1) - \mathbf{j}(1 \cdot 4 - (-1)(-...
= \mathbf{i}(8 + 1) - \mathbf{j}(4 - 2) + \mathbf{k}(1 + 4)
= 9\mathbf{i} - 2\mathbf{j} + 5\mathbf{k} = \begin{pmatrix} 9 \\ -2 \\...
Now compute its magnitude:
\|\mathbf{r} \times \mathbf{s}\| = \sqrt{9^2 + (-2)^2 + 5^2} = \sqrt{8...
Thus, the area is:
\boxed{\sqrt{110}}

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