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Question
Using Euler’s formula, find the values of a, b, c and d.
| Faces | a | 5 | 20 | 6 |
| Vertices | 6 | b | 12 | d |
| Edges | 12 | 9 | c | 12 |
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Solution
| Faces | a | 5 | 20 | 6 |
| Vertices | 6 | b | 12 | d |
| Edges | 12 | 9 | c | 12 |
(i) a + 6 – 12 = 2
⇒ a = 2 – 6 + 12
= 14 – 6
= 8
(ii) b + 5 – 9 = 2
⇒ 6 = 2 + 9 – 5
= 6
(iii) 20 + 12 – c = 2
⇒32 – c = 2
⇒ c = 32 – 2
⇒ c = 30
(iv) 6 + d – 12 = 2
⇒ d – 6 = 2
⇒ d = 2 + 6
= 8
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