Exercise 1.1.11

Question

Four corners of this unit cube are $(0,0,0),(1,0,0),(0,1,0),(0,0,1)$. What are the other four corners? Find the coordinates of the center point of the cube. The center points of the six faces are . The cube has how many edges?

Prakash Anand · Accepted Answer

Four more comers $(1,1,0),(1,0,1),(0,1,1),(1,1,1)$. The center point is $\left(\frac{1}{2}, \frac{1}{2}, \frac{1}{2}\right)$. Centers of faces are $\left(\frac{1}{2}, \frac{1}{2}, 0\right),\left(\frac{1}{2}, \frac{1}{2}, 1\right)$ and $\left(0, \frac{1}{2}, \frac{1}{2}\right),\left(1, \frac{1}{2}, \frac{1}{2}\right)$ and $\left(\frac{1}{2}, 0, \frac{1}{2}\right),\left(\frac{1}{2}, 1, \frac{1}{2}\right)$.

Exercise 1.1.11

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Exercise 1.1.11

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