Section 12.1 ~ Introduction to Solids
Topics in this lesson:
• polyhedron
• face/edge/vertex/base
• platonic solids
• cross section
Objective: To identify solids and their parts.
Types of Solids
Polyhedra
Not Polyhedra
Vocabulary
polyhedron (plural = polyhedra) ­ a solid that is bounded by polygons that enclose a single region of space
faces ­ the polygons on a polyhedron
edge ­ a line segment formed by the intersection of two faces
vertex ­ a point where three or more edges meet
bases of a prism ­ congruent polygons in parallel planes
base of a pyramid ­ the polygon used to name the pyramid
regular polyhedron ­ a polyhedron whose faces are all congruent regular polygons
*There are 5 of these ­ see Platonic Solids on back.
12.1
Classifying Solids
A polyhedron is named with its base and whether it's a prism or pyramid.
Platonic Solids
The five regular polyhedra
*The 5 platonic solids have special names.
Example 1
Tell whether the solid is a polyhedron. If it is, name the polyhedron and find the number of faces, vertices, and edges.
12.1
Euler's Theorem
pronounced "oi'­ler"
The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2
Example 2
Find the number of faces, vertices, and edges of the polyhedron shown. Check your answers using Euler's Theorem.
check
faces = _____
vertices = _____
edges = _____
Example 3
Is it possible for a polyhedron to have 16 faces, 34 vertices, and 50 edges?
Vocabulary
cross section ­ the intersection of a plane and a solid
12.1
Example 4
Describe the shape formed by the intersection of the plane and the solid.
The cross section is a _____________________.
a.
b. c.
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d.
p. 798, #2-4, 6, 12-14, 16,
18, 20, 28, 30, 32, 40
12.1