1. Section 12-1 Exploring Solids

2. Polyhedron Three dimensional closed figure formed by joining three or more polygons at their side. Plural: polyhedra

3. Parts of a Polyhedron

4. Face: Each polygon of the polyhedron Edge: A line segment along which two faces meet Vertex: A point where three or more edges meet

5. Regular polyhedron Has faces that are congruent regular polygons Example:

6. Convex Polyhedron If any two points on its surface can be connected by a segment that lies entirely inside or outside the polyhedron

7. Concave Polyhedron If the segment goes outside the polyhedron

8. Cross Section Intersection of a plane and a solid

9. A plane and a solid’s intersection forms different shapes.

10. Examples of a Plane and a Cube’s Cross Sections Square Triangle Trapezoid

11. Example of a Plane and a Sphere’s Cross Section Circle

12. Euler’s Theorem The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula:

13. Platonic Solids Five regular polyhedra: 1. Tetrahedron: 4 faces 2. Cube: 6 faces 3. Octahedron: 8 faces 4. Dodecahedron: 12 faces 5.Icosahedron: 20 faces

14. Regular Tetrahedron ____ faces, ____ vertices, ____ edges 464

15. Cube ____ faces, ____ vertices, ____ edges 8126

16. Regular Octahedron ____ faces, ____ vertices, ____ edges 6128

17. Regular Dodecahedron ____ faces, ____ vertices, ____ edges 1230 20

18. Regular Icosahedron ____ faces, ____ vertices, ____ edges 2012 30