1. 10-1 Vocabulary Face Edge Vertex Prism Cylinder Pyramid Cone Cube Net
Cross section

2. 10.1 Solid Geometry
Geometry

3. Defns. for 3-dimensional figures
Polyhedron – a solid bounded by polygons that enclose a single region of shape. (no curved parts & no openings!)
Faces – the polygons (or flat surfaces)
Edges – segments formed by the intersection of 2 faces
Vertex – point where three or more edges intersect

4. Types of Solids
Prism – 2  faces (called bases) in  planes. i.e. first example
Pyramid – has 1 base, all other edges connect at the same vertex. i.e. last example
Cone – like a pyramid, but base is a circle.
Cylinder – 2  circle bases. or
Sphere – like a ball.

5. Using Properties of Polyhedra
CONCEPT
SUMMARY
TYPES OF SOLIDS
Of the five solids below, the prism and the pyramid are polyhedra.
The cone, cylinder, and sphere are not polyhedra.
prism
pyramid
cone
cylinder
sphere

6. Ex 1: Classify each figure. Name the vertices, edges, & bases are there?
_______
v =
e =
b =
__________
______
v =
e =
b =

7. net

8. Describe the 3 dimensional figure from a net (pg. 655) Check it out
Ex. 2a.)
Ex. 2b.)

9. Ex. 3 Describe each cross section on pg. 656 Check it out

10. Assignment

11. Cross section

12. More definitions
Regular polyhedron – all faces are , regular polygons. i.e. a cube
Convex polyhedron – all the polyhedra we’ve seen so far are convex.
Concave polyhedron –
“caves in”
Cross section – the intersection of a plane slicing through a solid. Good picture on p.720

13. 5 regular polyhedra Also called platonic solids.
Turn to page 721 for good pictures at the top of the page.
Tetrahedron – 4 equilateral Δ faces
Cube (hexahedron) – 6 square faces
Octahedron – 8 equilateral Δ faces
Dodecahedron – 12 pentagon faces
Icosahedron – 20 equilateral Δ faces

14. Remember the first example?
Thm 12.1: Euler’s Theorem
The # of faces (F), vertices (V), & edges (E) are related by the equation:
F + V = E + 2
Remember the first example?
Let’s flashback…

15. Ex 1: How many faces, edges, & vertices are there?5 6 9
F + V = E + 2
5 + 6 = 9 + 2
11 = 11
F =
V =
E = 7 12
F + V = E + 2
7 + 7 =
14 = 14

16. Ex 2: A solid has 10 faces: 4 Δs, 1 square, 4 hexagons, & 1 octagon
Ex 2: A solid has 10 faces: 4 Δs, 1 square, 4 hexagons, & 1 octagon. How many edges & vertices does the solid have?
4 Δs = 4(3) = 12 edges
1 square = 4 edges
4 hexagons = 4(6) = 24 edges
1 octagon = 8 edges
F + V = E + 2
10 + V =
10 + V = 26
V = 16 vertices
48 edges total
But each edge is shared by 2 faces, so they have each been counted twice!
This means there are actually 24 edges on the solid. ( by 2)

17. Ex 3: A geodesic dome (like the silver ball at Epcot Center) is composed of 180 Δ faces. How many edges & vertices are on the dome?
180 Δs = 180(3) = 540 edges
540  2 = 270 edges
F + V = E + 2
180 + V =
180 + V = 272
V = 92 vertices

18. Assignment