Question

The equation

V+F−2=E, which relates the number of vertices, faces, and edges in a Platonic solid. Write an equation that makes it easier to find the number of vertices in a Dodecahedron, which has 30 edges.

A) V= 35 E−8
B) V= 25E−10
C) V= 23E−6
D) V= 32E−4

Answer 1

To find the number of vertices in a Dodecahedron with 30 edges, the equation V = 20 makes it easier to solve.

Step-by-step explanation:

To find the number of vertices in a Dodecahedron, we can rearrange the given equation V+F−2=E to solve for V. Since a Dodecahedron has 30 edges, we can substitute E in the equation as 30 and solve for V:

V + F - 2 = E

V + F - 2 = 30

V = 30 - F + 2

Since a Dodecahedron has 12 pentagonal faces, we substitute F as 12:

V = 30 - 12 + 2

V = 20

Therefore, the equation that makes it easier to find the number of vertices in a Dodecahedron with 30 edges is V = 20.