12'1Exploring Solids

1
Determine whether or not each of the following
solids is a polyhedron
2
Determine whether or not each of the following
solids is a polyhedron
No. The cylinder is not a polyhedron because it
contains curved edges.
3
Determine whether or not each of the following
solids is a polyhedron
Yes. The rectangular prism is an example of a
polyhedron.
4
Determine whether or not each of the following
solids is a polyhedron
No. The triangle is not a polyhedron because it
is not 3-dimensional.
5
Determine whether or not each of the following
solids is a polyhedron
Yes. The hexagonal prism is an example of a
polyhedron.
6
Find the number of faces, vertices, and edges
6 faces
8 vertices
12 edges
7
Find the number of faces, vertices, and edges
5 faces
6 vertices
9 edges
8
Find the number of faces, vertices, and edges
8 faces
12 vertices
18 edges
9
Find the number of faces, vertices, and edges
14 faces
24 vertices
36 edges
10
Theres a relationship between the number of
faces, vertices, and edges. The first person to
notice this was Leonhard Euler from Switzerland...



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• Just like polygons, a polyhedron can be...
• Regular or not regular
• Concave or convex
• There are only 5 types of regular polyhedra.
  They are called Platonic solids (named after
  Plato).

12
The 5 Platonic (Regular) Solids...
1) Tetrahedron (4 faces)
2) Hexahedron aka Cube (6 faces)
3) Octahedron (8 faces)
4) Dodecahedron (12 faces)
5) Icosahedron (20 faces)
13
One overhead sheet on cross sections...