A polyhedron is a hard with level faces(from Greek poly- meaning "many" and -hedron definition "face").
You are watching: What shape has 6 vertices 9 edges and 5 faces
CubeIts deals with are all squares
Triangular PrismIts deals with are trianglesand rectangles
DodecahedronWhat encounters does that have?
So no bent surfaces: cones, spheres and also cylinders room not polyhedrons.
Common Polyhedra
![]() ![]() ![]() ![]() | Platonic Solids | |
![]() ![]() | Prisms | |
![]() ![]() ![]() | Pyramids |
Note: the many of polyhedron is either polyhedrons or polyhedra
Many More
![]() | Explore 100s of animated Polyhedron Models. You can also see some photos of Polyhedra if girlfriend want. |
Counting Faces, Vertices and also Edges
When us count the number of faces (the level surfaces), vertices (corner points), and edges the a polyhedron we find an amazing thing:
The variety of facesplus the number of verticesminus the variety of edges amounts to 2
This deserve to be written nicely as a little equation:
F + V − E = 2
It is known as Euler"s Formula (or the "Polyhedral Formula") and also is really useful to make certain we have counted correctly!
Example: Cube
A cube has:
6 Faces8 Vertices (corner points)12 EdgesF + V − E = 6 + 8 − 12 = 2
Example: triangular Prism
This prism has:
5 Faces6 Vertices (corner points)9 EdgesF + V − E = 5 + 6 − 9 = 2
But over there are instances where the does not work! check out Euler"s Formula for more.
See more: How Much Do Pro Dart Players Make ? How Much Do Professional Dart Players Earn

Diagonals
A diagonal is a right line inside a shape that goes native one corner to an additional (but not an edge).
A polyhedron deserve to have lots of diagonals. Can you think the one there is no diagonals?
Geometry solid Geometry Platonic Solids prism