Euler's Formula

By: Tiffany Barney

Euler’s Formula states that F+V=E+2 where F= number of faces, V=number of vertices, E=number of edges of a polyhedron.

Polyhedron
Faces

Vertices

Edges

F+V=E+2

Eulerian or Not

Tetrahedron

4

4

6

4+4=6+2=8

Eulerian

Cube

6

8

12

6+8=12+2=14

Eulerian

Octahedron

8

6

12

8+6=12+2=14

Eulerian

Dodecahedron

12

20

30

12+20=30+2=32

Eulerian

Icosahedron

20

12

30

20+12=30+2=32

Eulerian

Pyramid

5

5

8

5+5=8+2=10

Eularian

Triangular Prism

5

6

9

5+6=9+2=11

Eularian

Pentagonal Pyramid

6

6

10

6+6=10+2=12

Eulerian

Pentagonal Prism

7

10

15

7+10=15+2=17

Eulerian

Two Joined Cubes

11

16

24

11+1624+2

Not Eulerian