Lalal

Platonic Solids
A Brief Introduction
A polygon is a two-dimensional shape bounded by straight line segments. A polygon is said to be regular if the edges are of equal length and meet at equalangles. A polygon is convex if the line connecting any two vertices remains inside or on the boundary of the polygon.

Convex

Not Convex

Question 1: Give an example of convex regular polygon.Question 2: Given any number n can you construct a regular polygon with n sides?

A Platonic Solid has the property that each face is an identical convex regular polygon, and that the same number ofpolygons meets at each corner. The Platonic solids feature prominently in the philosophy of Plato for whom they are named. The five solids were certainly known to the ancient Greeks and there isevidence that these figures were known long before then. There are only five Platonic Solids (can you explain why there are only five?) Tetrahedron: Four equilateral triangles, three meeting at eachcorner.

Cube: Six squares, three meeting at each corner.

Octahedron: Eight equilateral triangles, four meeting at each corner.

Dodecahedron: Twelve regular pentagons, three meeting at each corner.Icosahedron: Twenty equilateral triangles, five meeting at each corner.

Activity 1:
Record the following information in the table below: Platonic Solid Tetrahedron Cube Octahedron DodecahedronIcosahedron Vertices Edges Faces

Activity 2:
For each solid compute the following: Platonic Solid Tetrahedron Cube Octahedron Dodecahedron Icosahedron Vertices – Edges + Faces

What is yourobservation? ___________________________________________________ The formula Vertices – Edges + Faces = “your number from Activity 2” Is known as Euler’s Formula for Polyhedra.

Question 3: Do you seeany relation between the number of vertices, edges and faces of the
platonic solids?

A polyhedron (plural: polyhedra or polyhedrons) is a 3-dimensional geometric shape having flat faces that...