What shape has 21 faces and 14 vertices
Euler's formula:
V-E+F=2
14-E + 21 = 2
-E = -33
E = 33
To determine the shape with 21 faces and 14 vertices, we can use the Euler's formula. Euler's formula states that for any convex polyhedron (a three-dimensional solid with flat faces), the number of faces (F), vertices (V), and edges (E) are related by the equation F + V - E = 2.
So, in this case, we have F = 21 and V = 14. Let's use Euler's formula to find the number of edges (E):
F + V - E = 2
21 + 14 - E = 2
35 - E = 2
-E = 2 - 35
-E = -33
By multiplying both sides of the equation by -1, we get:
E = 33
Now that we have the number of edges, we can try to find a shape that satisfies these conditions. This particular shape is called a dodecahedron. A dodecahedron is a 12-faced polyhedron with 20 vertices and 30 edges. However, in this case, we need to find a shape with 21 faces and 14 vertices.
Based on these conditions, it seems that there is no known polyhedron that meets these criteria exactly. It is possible that the shape in question may be a non-convex polyhedron, a combination of multiple shapes, or not a three-dimensional shape at all.