A polyhedron has 30 edges and 12 vertices. How many faces does it have
A sphere is not a polyhedron because it has no edges, no vertices and no flat faces The word 'polyhedron' means many faces.
eight
In geometry, a pentahedron is a polyhedron with five faces. That can either be a square pyramid with 5 vertices, 8 edges and 5 faces or a triangular prism with 6 vertices, 9 edges and 5 faces.
Four faces, six edges and four vertices.
A polyhedron has 30 edges and 12 vertices. How many faces does it have
A sphere is not a polyhedron because it has no edges, no vertices and no flat faces The word 'polyhedron' means many faces.
It is a triangular prism that has 5 faces, 6 vertices and 9 edges
It has 6 vertices.
eight
6
Such a polyhedron cannot exist. According to the Euler characteristics, V + F - E = 2, where V = vertices, F = faces, E = edges. This would require that the polyhedron had only two faces.
12 vertices A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges.
v=60-20
The only thing that can be said that there must be at least 4 faces and at least 6 edges and that the polyhedron must satisfy the Euler criterion which requires that: Faces + Vertices = Edges + 2.
Oh, dude, it's like a math riddle! So, if a polyhedron has 10 more edges than vertices, we can use Euler's formula: Faces + Vertices - Edges = 2. Since we know the relationship between edges and vertices, we can substitute that in and solve for faces. So, it would have 22 faces. Math can be fun... sometimes.
If the object is a convex polyhedron, then, by Euler's characteristics, it should have 23 faces.