Question

Could a polyhedron exist with the given number of faces, vertices, and edges? Drag “yes” or “no” to each combination.10 faces, 7 vertices, 15 edges 12 faces, 20 vertices, 30 edges 6 faces, 4 vertices, 6 edges

Answer 1

$\begin{gathered} Polyhedron\text{ is possible if the given data satisfies the }Eulers\text{ formula,} \\ F\text{ + V - E = 2 } \\ \text{Where,} \\ F\text{ = Face , V = Vertices , E = Edges } \\ 1)\text{ }10faces,7vertices,15edges \\ 10\text{ + 7 - 15 = }2 \\ \text{Yes polyhedron is possible} \\ 2)\text{ }12faces,20vertices,30edges \\ 12\text{ + 20 - 30 = 2 } \\ \text{Yes polyhedron is possible} \\ 3)\text{ }6faces,4vertices,6edges \\ 6\text{ + 4 - 6 = 4 }\ne\text{ 2} \\ No\text{ polyhedron is not possible.} \end{gathered}$