Exploring Solids

1
12.1

• Exploring Solids

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Polyhedron

• Three dimensional closed figure formed by joining
  three or more polygons
• Example

3
Which of the following are polyhedrons?
No
Yes
Yes
Yes
No
Yes
4

• Face sides of a polyhedron that enclose a single
  region of space
• Edge a line segment formed by the intersection
  of two faces
• Vertex a point where three or more edges meet

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Example
vertex
face
edge
Faces 6 Vertices 8 Edges 12
6
Identify the number of faces, vertices, and edges
for each figure.
Faces- 5 Vertices- 6 Edges- 9
Faces- 6 Vertices- 8 Edges- 12
Faces- 7 Vertices- 10 Edges- 15
Faces- 6 Vertices- 8 Edges- 12
Faces- 6 Vertices- 6 Edges- 10
Faces- 8 Vertices- 12 Edges- 18
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Eulers Theorem

• The number of faces F, vertices V, and edges E of
  a polyhedron are related by
• F V 2 E

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Use Eulers Theorem to find the unknown number
Faces Vertices 16 Edges 22
Faces 5 Vertices Edges 9
Faces Vertices 10 Edges 15
Faces 20 Vertices 12 Edges
8
7
6
30
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• A polyhedron is regular if all of its faces are
  congruent regular polygons.
• A polyhedron is convex if any two points on its
  surface can be connected by a segment that lies
  entirely inside or on the polyhedron.

regular convex
irregular concave
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• Cross Section the intersection of the plane and
  the solid

11
Describe the shape formed by the intersection of
the plane and the cube
pentagon
triangle
square