Use Euler’s formula to answer the question.
A polyhedron has 12 edges and 6 faces, how many vertices does it have?
Euler's formula state that for a polyhedrons,
V+F=E+2
V=number of vertices
E=number of edges
F=number of faces
Take a tetrahedron, which has
6 edges, 4 vertices and 4 faces
4+4=6+2
For the given polyhedron,
E=12
F=6
So solve for V in
F+V=E+2
Post your answer for a check if you wish.
Euler's formula states that for any polyhedron with V vertices, E edges, and F faces, the relationship is V + F = E + 2.
Given that the polyhedron has 12 edges and 6 faces, we can substitute these values into Euler's formula to find the number of vertices.
V + 6 = 12 + 2
Simplifying the equation, we have:
V + 6 = 14
Subtracting 6 from both sides, we get:
V = 8
Therefore, the polyhedron has 8 vertices.
Euler's formula, also known as Euler's polyhedron formula, states that for any convex polyhedron, the number of vertices (V), the number of edges (E), and the number of faces (F) are related by the equation V - E + F = 2.
To use Euler's formula to answer the question, we already know the values of E (12) and F (6). We need to find the value of V.
By substituting the known values into Euler's formula, we get V - 12 + 6 = 2.
To find V, we can rearrange the equation to solve for V:
V - 12 + 6 = 2
V - 6 = 2
V = 2 + 6
V = 8.
Therefore, the polyhedron has 8 vertices.