Wednesday, January 4, 2012

vertices,edges and faces


Vertices, Edges and Faces

Vertex, Edge and Face
A vertex is a corner
An edge joins one vertex with another
A face is an individual surface
Let us look more closely at each of those:

Vertices

vertex (plural: vertices) is a point where two or more straight lines meet.
It is a Corner.
This tetrahedron has 4 vertices.
Vertex
Pentagon verticesAnd this pentagon has 5 vertices

Edges

Edges
An edge is a line segment that joins two vertices.
This tetrahedron has 6 edges.
And this pentagon has 5 edges
Pentagon edges
circle
It can also be the boundary of a shape.
Such as the circumference of a circle.

Faces

Faces
A face is any of the individual surfaces of a solid object.
This tetrahedron has 4 faces (there is one face you can't see)

Euler's Formula

For many solid shapes the
  • Number of Faces
  • plus the Number of Vertices
  • minus the Number of Edges
always equals 2
This can be written: F + V - E = 2
cube
Try it on the cube:
A cube has 6 Faces, 8 Vertices, and 12 Edges,
so:
6 + 8 - 12 = 2
(To find out more about this read Euler's Formula.)

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