Mathematics

Can a polyhedron have 15 faces, 30 edges and 20 vertices ?

3D in 2D

2 Likes

Answer

F = 15, V = 20, E = 30

According to Euler's formula,

F + V - E = 2

F + V - E = 15 + 20 - 30

= 35 - 30

= 5

⇒ F + V - E is not equal to 2.

Hence, a polyhedron cannot have 15 faces, 30 edges and 20 vertices.

Answered By

2 Likes

Related Questions

Assertion (A) : The number of edges in a rectangular pyramid = 8.
Reason (R) : In a triangular prism, the number of vertices is one more than number of sides and the number of faces is one less than number of sides.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are false.
A is true, but R is false.
A is false, but R is true.
View Answer Bookmark Now