Practice problems:

1. A polyhedron is made of 4 triangles, 3 squares and 1 hexagon. How many Faces, Edges and Vertices does it have?

Faces: 4+3+1=8 faces

Edges: 4*3+3*4+1*6=30; 30/2=15

(3 sides on a triangle times 4 triangles; 4 sides on a square times 3 squares; 6 sides on a hexagon times 1 hexagon makes 30 edges before you put the faces together. Putting the faces together combines 2 edges into 1 edge, so you have half as many edges in the poyhedra after it is assembled)

V+F-E=2 (this is Euler's formula)
V+8-15=2 (plug in the numbers you know)
V+ -7=2 (find the number you don't know yet)
V=2+7=9

2. A polyhedron is made of 4 triangles, 5 squares and 1 octagon. How many Faces, Edges and Vertices does it have?

Faces: 4+5+1=10 faces

Edges: 4*3+5*4+1*8=40; 40/2=20

V+F-E=2
V+10-20=2
V+ -10=2
V=2+10=12

3. A polyhedron is made of 4 triangles, 4 squares and 2 pentagons. How many Faces, Edges and Vertices does it have?

Faces: 4+4+2=10 faces

Edges: 4*3+4*4+2*5=40; 38/2=19

V+F-E=2
V+10-19=2
V+ -9=2
V=2+9=11