Question 76
A regular dodecahedron is a convex polyhedron such that its faces are regular pentagons. It has 20 vertices and 3 edges connected to each vertex. (As you see in the picture.)
Suppose that we have marked 10 vertices of a regular dodecahedron.
a) Prove that we can rotate the dodecahedron in such a way that the dodecahedron is mapped to itself and at most four marked vertices are mapped to a marked vertex.
b) Prove that number 4 cannot be replaced with number 3 in the previous part.
Suppose that we have marked 10 vertices of a regular dodecahedron.
a) Prove that we can rotate the dodecahedron in such a way that the dodecahedron is mapped to itself and at most four marked vertices are mapped to a marked vertex.
b) Prove that number 4 cannot be replaced with number 3 in the previous part.