polyhedron

a three-dimensional figure

whose surfaces are polygons

faces

edge

vertex

Euler’s Formula

The number of faces (F), vertices (V), and

edges (E) of a polyhedron three-dimensional are

related by the formula

F + V = E + 2

Example

A polyhedron has 8 faces and 18 edges. How many vertices

does this polyhedron have ?

F + V = E + 28 + V = 18 + 28 + V = 20-8 -8

V = 12

Euler’s Formula

The number of faces (F), vertices (V), and

edges (E) of a polyhedron in two-

dimensional are related by the formula

F + V = E + 1

How many regions, vertices and

segments are on the following polyhedron in 2-dimension space

?

regions

1

2

3

4

5

6

7

8 8

segments

1

2

3

4

5

6

7

8

9

10 11

12

13

14

15

16

17

18

19 20

21 22 23

24

25 26

2728 29

29

How many regions, vertices and

segments are on the following polyhedron in 2-dimension space

?

regions 8 segments

1

2

3

4

5 6

7

8

9

10 11

12

13

14

15

16 17

18

19

20 21 22

22

29

vertices

Cross sections

Slicing the polyhedron with a plane and examining the resulting figure.

AssignmentWorkbook

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