A polyhedron has 15 vertices and 31 edges. How many faces does it have?

faces-vertexes+edges=2

This is Euler's formula.

To find the number of faces of a polyhedron, you can use Euler's formula. According to Euler's formula, for any polyhedron, the number of vertices (V), minus the number of edges (E), plus the number of faces (F), equals 2.

Given that the polyhedron in question has 15 vertices (V) and 31 edges (E), we can plug these values into the formula:

V - E + F = 2

Substituting the known values:

15 - 31 + F = 2

Simplifying the equation:

-16 + F = 2

To isolate F, we can add 16 to both sides of the equation:

F = 2 + 16

F = 18

Therefore, the polyhedron has 18 faces.