Polyhedrons

A polyhedron is a solid with flat faces
(from Greek poly- meaning "many" and -hedron meaning "face").

Each face is a polygon (a flat shape with straight sides).

Examples of Polyhedra:

cubeCube
Its faces are all squares
triangular prismTriangular Prism
Its faces are triangles
and rectangles
dodecahedronDodecahedron
What faces does it have?

No curved surfaces: cones, spheres and cylinders are not polyhedrons.

Common Polyhedra

cube or hexahedron square prism Cubes and
Cuboids (Volume
of a Cuboid)
tetrahedron cube or hexahedron octahedron dodecahedron icosahedron Platonic Solids
triangular prism square prism pentagonal prism Prisms
triangular pyramid square pyramid pentagonal pyramid Pyramids

Note: the plural of polyhedron is either polyhedrons or polyhedra

Many More

Animated Polyhedron Models  

Explore 100s of Animated Polyhedron Models.

You can also see some Images of Polyhedra if you want.

Counting Faces, Vertices and Edges

When we count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron we discover an interesting thing:

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 − E = 2

It is known as Euler's Formula (or the "Polyhedral Formula") and is very useful to make sure we have counted correctly!

cube

Example: Cube

A cube has:

  • 6 Faces
  • 8 Vertices (corner points)
  • 12 Edges

F + V − E = 6 + 8 − 12 = 2

triangular prism

Example: Triangular Prism

This prism has:

  • 5 Faces
  • 6 Vertices (corner points)
  • 9 Edges

F + V − E = 5 + 6 − 9 = 2

But there are cases where it does not work! Read Euler's Formula for more.

 

diagonal

Diagonals

A 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
Geometry Solid Geometry Platonic Solids Prisms