Exploring Solids

1
Exploring Solids
2
What is a Polyhedron?
Non-Polyhedrons
Polyhedrons
3
Do you notice a difference?
Non-Polyhedrons
Polyhedrons
4
Polyhedrons

• A solid that is bounded by polygons that enclose
  a single region of space
• There are two main types of solids
• Prisms and Pyramids

5
Parts of a Polyhedron
6
Face

• The polygons that make up the sides of a
  polyhedron

7
Edge

• A line segment formed by the intersection of 2
  faces

8
Vertex

• A point where 3 or more edges meet

9
Name the Polyhedron and find the number of Faces,
Vertices, and Edges
a.
b.
c.
10
a.
b.
c.
F 5 V 5 E 8
F 5 V 6 E 9
F 8 V 12 E 18
11
a.
b.
c.
F 5 V 5 E 8
F 5 V 6 E 9
F 8 V 12 E 18
Does anybody see a pattern?
12
Eulers Theorem
F V E 2
13
Eulers Theorem
F V E 2
Example
14
Eulers Theorem
F V E 2
Example
F 6, V 8, E 12
15
Eulers Theorem
F V E 2
Example
F 6, V 8, E 12
6 8 12 2
16
Eulers Theorem
F V E 2
Example
F 6, V 8, E 12
6 8 12 2
14 14
17
Example Use Eulers Theorem to find the value of
n
Faces 5 Vertices n Edges 8
18
Example Use Eulers Theorem to find the value of
n
Faces 5 Vertices n Edges 8
F V E 2 5 n 8 2 5 n 10 n 5