Question

A polyhedron has 6 faces and 8 vertices. By Euler's formula find the number of edges in the polyhedron and then name the polyhedron .

Answer 1

Answer:

It is a cuboid or quadrilaterally-faced hexahedron.

Step By Step Explanation:

There is no unique formula for getting the figure. However, according to Euler's Polyhedral Formula, in a convex polyhedra, if

V is the number of vertices,

F is number of faces and

E is number of edges than

V – E + F = 2

It is apparent that with 6 faces, 8 vertices, and 12 edges, then

8 – 12 + 6 = 2

Hence it is a valid polyhedra.

However, it is evident that the figure is a cuboid or quadrilaterally-faced hexahedron, as it too has 6 faces, 8 vertices, and 12 edges.

#SPJ2

Answer 2

Answer:

It has twelve edges.

The polyhedron is cube.

Step-by-step explanation:

The Euler's formula is given as:

$F + V = E + 2$

F is the number of faces, V the number of vertices, and E the number of edges.

Now,

It is given that a polyhedron has six faces and eight vertices.

So,

$F=6$

$E=8$

Using it in formula, we get

$6+8=E+2$

$E=6+8-2$

$E=12$

So, there are $12$ edges.

As there are six faces, wight vertices and twelve edges, the polyhedron is cube.

#SPJ2