18. Wire cube. Each edge of the wire cube has a resistance of 1 Ohm. What is the resistance between two opposite vertices of this cube?

![](https://cdn.mathpix.com/cropped/2024_05_21_2b40d984baf9da275c68g-015.jpg?height=299&width=554&top_left_y=2152&top_left_x=754)
18. Suppose the edges of our cube are hinged at the vertices. If we lift the cube by one of its vertices, the edges will sag, forming a structure consisting of three sequentially connected groups of conductors, each of which in turn consists of three, six, and three parallel-connected conductors*. The ends of the resulting structure are precisely the opposite vertices of the original cube. Therefore, the total resistance between the opposite vertices of the cube is $\frac{1}{3}+\frac{1}{6}+\frac{1}{3}=\frac{5}{6}$ Ohms.

![](https://cdn.mathpix.com/cropped/2024_05_21_2b40d984baf9da275c68g-081.jpg?height=619&width=223&top_left_y=1004&top_left_x=922)