Icosahedron and dodecahedron

In your book, Maths Mela (Chapter 7, Shapes and Patterns), we make two solid shapes from the nets at the end of the book: the icosahedron and the dodecahedron. The book says their names tell you something once you count their faces. 'Icosa' means twenty, and an icosahedron has 20 faces. 'Dodeca' means twelve, and a dodecahedron has 12 faces.

Every face of an icosahedron is a triangle with 3 equal sides (an equilateral triangle), and all 20 faces are the same. Every face of a dodecahedron is a pentagon with 5 equal sides (a regular pentagon), and all 12 faces are the same.

A vertex is a corner point where faces meet. At every vertex of an icosahedron, 5 triangles meet. At every vertex of a dodecahedron, 3 pentagons meet. In each solid, the same number of faces meet at every vertex.

How can we count the edges without missing one or counting one twice? Count the sides of all the faces, then remember that each edge is shared by 2 faces, so every edge was counted twice. The icosahedron has 20 faces with 3 sides each: 20 × 3 = 60 sides, and half of 60 is 30 edges. The dodecahedron has 12 faces with 5 sides each: 12 × 5 = 60 sides, and half of 60 is 30 edges. Both solids have 30 edges!