# Can a polyhedron have 10 faces , 20 edges, and 15 vertices ?

2
by zoyastarfarooqi
14 or 15 vertices ?

2015-01-20T20:02:23+05:30
no a polyhedron cant have 10 faces , 20 edges, and 15 vertices as eulers formula is not satisfied
euler's  formula = faces+ vertices-edges = 2
10 + 15-20 = 2
25-20  = 2
5
2
so it cant have
10 faces , 20 edges, and 15 vertices
2015-01-20T20:11:21+05:30
No.It can't have 10 faces , 20 edges, and 15 vertices as The formula i.e. Euler's formula isn't being satisfied.
According to the formula....
(F+V)-E=2
Where,
F=>faces=10
E=>edges=20
V=>vertices=15

(F+V)-E=2
(10+15)-20=2
25-20=2
but
5
≠2
so,the Euler's formula is not satisfied.

Therefore,A polyhedron cannot have
10 faces , 20 edges, and 15 vertices.