Chapter 4.5, Problem 30MS

Here we celeb rate the power of algebra as a powerful way of finding unknown quarnities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.

Rhombi-what? There is a semi-regular solid with 62 faces called (ironically)the small rhombicosidodecahedron (rhombi -cosidodecahedron). We’ll call it the Small R. It has half again as many square faces as triangular faces, and three fifths as many pentagonal faces as triangular faces. Find the number of faces the Small R has of each type.