12.1 Exploring Solids

Polyhedron

Platonic Solids

Cross Section

Definition of a Polyhedron

A polyhedron is a solid formed by many plane faces.

Convex Polyhedron

Convex Polyhedron are polyhedrons where any two points can be connected by a line segment

Convex NonConvex

Faces, Edges and Vertices

A Cube has 6 Faces, 12 Edges

and 8 Vertices.

face edge

vertex

Cross sectionThe cutting of a polyhedron or cone by a

plane giving different shapes.

Regular Polyhedron

A regular polyhedron has regular polygons for faces

Platonic Solids are regular polyhedrons

Can you think of any use of a Icosahedrons?

Euler’s Theorem

The number of faces + number of vertices equals the number of edges plus 2.

Icosahedrons has 20 faces, 12 vertices.

How many

Edges?

Euler’s Theorem

The number of faces + number of vertices equals the number of edges plus 2.

Icosahedrons has 20 faces, 12 vertices.

How many

Edges?

E

E

E

30

232

21220

How many Edges on this shape?

Edge = ½(Shape edges times Number of Shapes + Shape edges times Number of Shapes…..)

How many Edges on this shape?

Edge =

½ (8 sides* 6 + 4 sides* 10 + 6 sides * 8)

How many Edges on this shape?

Edge = 68

½ (8 sides* 6 + 4 sides* 10 + 6 sides * 8)

How many Vertices on this shape?

Edge = 68, Faces = (6 +10 + 8) = 24

How many Vertices on this shape?

Edge = 68, Faces = (6 +10 + 8) = 24

24 + V = 68 + 2

24 + V = 70

V = 46

Homework

Page 723 – 726

# 10 – 30 even,

32 – 35 , 42- 52,

54, 55