A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is :

All edges have equal resistance. Total wire resistance = R.
Number of edges in a tetrahedron = 6

So resistance of each edge:

$$r=\frac{R}{6}$$

Now find equivalent between two vertices (say A and B).

By symmetry, the other two vertices are at same potential → no current flows between them.

So that edge can be ignored.

Now circuit reduces to:

• Direct edge A-B: r
• Two identical paths A → (top nodes) → B
  Each path has 2 resistors in series → 2r

So we have 3 parallel paths:

$$R_{eq}=r\parallel2r\parallel2r$$

$$R_{eq}=\frac{r}{2}$$

Substitute $$r=R/6$$

$$R_{eq}=\frac{R}{12}$$