Question

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

Answer 1

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$\neq$ 2
so it cant have  10 faces , 20 edges, and 15 vertices 

Answer 2

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.