Question

Using Euler's formula, find the values of a, b, c and d.

Answer 1

Faces	$a$	$5$	$20$	$6$
Vertices	$6$	$b$	$12$	$d$
Edges	$12$	$9$	$c$	$12$

(i) We can write it as
$a+6-12=2$
By further calculation
$a=2-6+12$
(ii) We can write it as
$b+5-9=2$
By further calculation
$b=2+9-5$
$b=6$
(iii) We can write it as
$20+12-c=2$
By further calculation
$32-c=2$
$c=32-2=30$
(iv) We can write it as
$6+d-12=2$
By further calculation
$d-6=2$
$d=2+6=8$