Gven
no of vertices = 10
The no of edges on each face = 3
Let the no of vertices be 'n' ,no of edges be 'e' , the no of regeions ( faces) be ' r ' .
But
The sum of the degrees of the regions ( faces ) = 2( no of edges)
d(R1) + d(R2) + d(R3) +..............(r times) = 2e
3+3+3+......................(r times )= 2e
3r = 2e
r = 2e/3
By euler's formula we have
n - e + r = 2
10 - e + 2e/3 = 2
10 - e/3 = 2
30 - e = 6
e = 24
The no of edges = 24.