Euler’s Law by Hannah S
Daily Posts February 27th, 2007
If you look at the relationship between the faces, edges, and vertices of a polyhedron, you see that the sum of the faces and edges is equal to 2 more than the number of edges. Euler turned this fact into a formula.
Euler’s Law:
F+V=E+2
(F= faces E= edges V= vertices)
Examples:
1) A prism has 12 faces and 6 vertices. How many edges does it have?
F+V=E+2
12+6=E+2
18=E+2
E=16
2) A pyramid has 5 faces and 9 edges. How many vertices does it have?
F+V=E+2
5+V=9+2
5+V=11
V=6
3) A polyhedron has 13 edges and 7 vertices. How many faces does it have?
F+V=E+2
F+7=13+2
F+7=15
F=8
