1. 12.1
Exploring Solids

2. 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

5. Example:
vertex
face
edge
Faces: 6 Vertices: 8 Edges: 12

6. Identify the number of faces, vertices, and edges for each figure.

7. Euler’s Theorem: F + V – 2 = E
The number of faces F, vertices V, and edges E of a polyhedron are related by
F + V – 2 = E

8. Use Euler’s 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

9. 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

10. 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