Question

The dodecahedron and icosahedron are dual to each other? True or False?

Answer 1

Around each vertex of the icosahedron there are five triangles, and the centers of these five triangles when connected form a regular pentagon. The icosahedron has 12 vertices, so we obtain a regular arrangement of 12 regular pentagons, three at each vertex. This is the regular polyhedron predicted as the regular dodecahedron

The regular dodecahedron has 20 vertices, with three pentagons at each vertex. The centers of the pentagons will then give 20 equilateral triangles, forming a regular icosahedron.

Hence they both are dual of each other