IMO Shortlist 1985 problem 2
Dodao/la:
arhiva2. travnja 2012. A polyhedron has
![12](/media/m/e/f/6/ef6c8e9eecc5ee3d49031ee4f0e20f98.png)
faces and is such that:
(i) all faces are isosceles triangles,
(ii) all edges have length either
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
or
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
,
(iii) at each vertex either
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
or
![6](/media/m/e/e/e/eeec330d59a70f8ed1d6882474cb02a3.png)
edges meet, and
(iv) all dihedral angles are equal.
Find the ratio
%V0
A polyhedron has $12$ faces and is such that:
(i) all faces are isosceles triangles,
(ii) all edges have length either $x$ or $y$,
(iii) at each vertex either $3$ or $6$ edges meet, and
(iv) all dihedral angles are equal.
Find the ratio $x/y.$
Izvor: Međunarodna matematička olimpijada, shortlist 1985