1. Polyhedron Platonic Solids Cross Section
12.1 Exploring Solids
Polyhedron
Platonic Solids
Cross Section

2. Definition of a Polyhedron
A polyhedron is a solid formed by many plane faces.

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

4. Faces, Edges and Vertices
A Cube has 6 Faces, 12 Edges
and 8 Vertices.

5. Cross section
The cutting of a polyhedron or cone by a plane giving different shapes.

6. Regular Polyhedron
A regular polyhedron has regular polygons for faces

7. Platonic Solids are regular polyhedrons

8. Can you think of any use of a Icosahedrons?

9. 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?

10. 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?

11. How many Edges on this shape?
Edge = ½(Shape edges times Number of Shapes + Shape edges times Number of Shapes…..)

12. How many Edges on this shape?
½ (8 sides* sides* sides * 8)

13. How many Edges on this shape?
½ (8 sides* sides* sides * 8)

14. How many Vertices on this shape?
Edge = 68, Faces = ( ) = 24

15. How many Vertices on this shape?
Edge = 68, Faces = ( ) = 24
24 + V =
24 + V = 70
V = 46

16. Homework
Page 723 – 726
# 10 – 30 even,
32 – 35 , ,
54, 55