Question

In each of the following determine whether a polyhedron can have a) 5 faces, 13 edges, 10 vertices b) 18 faces, 25 edges, 12 vertices​

Answer 1

Answer:

a) It can be a polyhedron

b) It cannot be a polyhedron

Step-by-step explanation:

a) Using Euler's Formula,

F + V - E = 2

F = 5, V = 10, E = 13

F + V - E = 5 + 10 - 13 = 15 - 13 = 2

∵ It obeys Euler's formula

∴ A polyhedron can have 5 faces, 13 edges and 10 vertices

b) Using Euler's Formula,

F + V - E = 2

F = 18, V = 12, E = 25

F + V - E = 18 + 12 - 25 = 30 - 25 = 5

∵ It does not obey Euler's formula

∴ A polyhedron cannot have 18 faces, 25 edges, 12 vertices​

Hope it helps...