1
Question
Using Euler’s formula, find the unknown.
Faces
?
5
20
Vertices
6
?
12
Edges
12
9
?
Using Euler’s formula, find the unknown.
|
Faces |
? |
5 |
20 |
|
Vertices |
6 |
? |
12 |
|
Edges |
12 |
9 |
? |
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Solution
By Euler’s formula, we have
F + V − E = 2
(i) F + 6 − 12 = 2
F − 6 = 2
F = 8
(ii) 5 + V − 9 = 2
V − 4 = 2
V = 6
(iii) 20 + 12 − E = 2
32 − E = 2
E = 30
Thus, the table can be completed as
Faces
8
5
20
Vertices
6
6
12
Edges
12
9
30
​
By Euler’s formula, we have
F + V − E = 2
(i) F + 6 − 12 = 2
F − 6 = 2
F = 8
(ii) 5 + V − 9 = 2
V − 4 = 2
V = 6
(iii) 20 + 12 − E = 2
32 − E = 2
E = 30
Thus, the table can be completed as
|
Faces |
8 |
5 |
20 |
|
Vertices |
6 |
6 |
12 |
|
Edges |
12 |
9 |
30 |
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