A polyhedron is a solid shape with flat faces and straight edges.
Each face is a polygon (a flat shape with straight sides).
comes from Greek poly- meaning "many" and -hedron meaning "face".
The plural can be polyhedra or polyhedrons.
Examples of Polyhedra: CubeIts faces are all squares
Triangular PrismIts faces are triangles
and rectangles
DodecahedronWhat faces does it have?
No curved surfaces: cones, spheres and cylinders are not polyhedra.
Common Polyhedra Many More Counting Faces, Vertices and EdgesWhen we count the faces (the flat surfaces), vertices (corner points), and edges of a polyhedron we dfind a neat pattern:
The number of faces
plus the number of vertices
minus the number of edges equals 2
This can be written neatly as a little equation:
F + V â E = 2It is known as Euler's Formula (or the "Polyhedral Formula") and is very useful to make sure we have counted correctly!
Example: CubeA cube has:
F + V â E
= 6 + 8 â 12
= 2
This prism has:
F + V â E
= 5 + 6 â 9
= 2
Example: HoneycombBees store honey in hexagonal prisms.
The ends are hexagons and the 6 sides are rectangles.
Each prism has 8 faces, 12 vertices and 18 edges.
Can you try to use Euler's Formula on this?
But there are cases where it does not work! Read Euler's Formula for more.
DiagonalsA diagonal is a straight line inside a shape that goes from one corner to another (but not an edge).
A polyhedron can have lots of diagonals. Can you think of one without diagonals?
6082, 6083, 6084, 6085, 6086, 6087, 2145, 2146, 2147, 3374, 3375, 3376
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