Question

Select the correct relationship between the number of vertices (V), edges (E), and faces (F) for a polyhedron.

A) V+F−E=2
B) F+E−V=2
C) V+F+E=2
D) E+V−F=2

Answer 1

The correct relationship between the number of vertices (V), edges (E), and faces (F) for a polyhedron is V+F−E=2, known as Euler's formula.

Step-by-step explanation:

The correct relationship between the number of vertices (V), edges (E), and faces (F) for a polyhedron is option A) V+F−E=2.

This relationship is known as Euler's formula for polyhedra.

Euler's formula states that for any convex polyhedron, the number of vertices plus the number of faces minus the number of edges is always equal to 2.

For example, if a polyhedron has 6 vertices, 8 edges, and 5 faces, we can substitute these values into Euler's formula: 6 + 5 - 8 = 2.