CK12 - Geometry

If we makea tablethat summarizesthe data from eachof the figureswe get:

Figure Vertices Faces Edges

Squarepyramid 5 5 8

Rectangularprism 8 6 12

Octahedron 6 8 12

Pentagonalprism 10 7 15

Do you see a pattern?Calculatethe sum of the numberof verticesand edges.Thencomparethat sum to
the numberof edges:

Figure V F E V + F

squarepyramid 5 5 8 10

rectangularprism 8 6 12 14

octahedron 6 8 12 14

pentagonalprism 10 7 15 17

Do you see the pattern?The formulathat summarizesthis relationshipis namedaftermathematician
LeonhardEuler. Euler’s formulasays,for any polyhedron:

Euler'sFormulafor Polyhedra

or

You can use Euler’s formulato find the numberof edges,faces,or verticesin a polyhedron.

Example 4

Countthe numberof faces,edges,and verticesin the figure.Doesit conformto Euler’s formula?