Question

If a crystal contains 5 faces and 8 edges, the number of vertices in the crystal is _________.

Hint:

Euler’s formula applies to convex polyhedra and can help determine one of the elements (vertices, edges, or faces) if the others are known.

Answer 1

Correct Answer: 5

Step 1: Apply Euler's Formula.
Euler's formula for polyhedra is: \[ V - E + F = 2, \] where \(V\) is the number of vertices, \(E\) is the number of edges, and \(F\) is the number of faces. Substituting the given values: \[ V - 8 + 5 = 2, \] \[ V - 3 = 2, \] \[ V = 5. \] Step 2: Conclusion.
The number of vertices in the crystal is 6.