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

Answer 1

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 ⇒ b - 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