A

To find the equivalent resistance between points 1 and 7 in the cube, we analyze the arrangement of resistors. Each edge of the cube represents a resistor of 6 Ω.
Step 1: Identify the paths between points 1 and 7. There are multiple paths: 1-2-3-7, 1-2-6-7, 1-4-3-7, and 1-4-5-7.
Step 2: Determine the resistances in each series and parallel connection. Paths like 1-2-3-7 and 1-4-3-7 are in series with the resistors along the edges. Each series path can be calculated, resulting in resistances like 6 + 6 + 6 = 18 Ω.
Paths combine in parallel since they connect between the same nodes. Analyzing combinations will simplify to a total resistance of 6/3 = 2 Ω when summed.
Step 3: Calculate the total effective resistance. For multiple resistors arranged in parallel and series, use the formula \( R_{total} = \frac{1}{\sum \frac{1}{R_i}} \) for parallel ones. After calculating all paths, the resultant resistance seen from 1 to 7 equates to 6 Ω overall in this structure.
Therefore the equivalent resistance is 6 Ω.