1. 10-1 Space Figures and Nets
5/17/17
POLYHEDRON: a three-dimensional figure whose surfaces are polygons
Each polygon is called a FACE.
EDGE: a segment that is formed by the intersection of two faces
VERTEX: a point where three or more edges intersect
NET: a two-dimensional pattern that you can fold to form a three-dimensional figure

2. CUBE: a polyhedron with six faces
edge
face
vertex
Ex: Is the pattern a net for a cube? If so, name the letters that will appear on opposite faces. F
A B C D E
YES. A and C, B and D, E and F are on opposite faces. .

3. F B C Sketch the three dimensional figure that corresponds to the net.
Is the pattern a net for a cube? If so, name the two letters that will appear on opposite faces. A
 B & E, but this will NOT make a cube!!! B D E C F D F F C
B & D, A & C, E & F B
A  A B C D E E

4. Euler’s Formula F + V = E + 2 F = # of faces V = # of vertices
pronounced “Oiler” as in…
F + V = E + 2
F = # of faces
V = # of vertices
E = # of edges
This polyhedron has 2 hexagons and 6 rectangles. Find the # of vertices.
… without simply counting them. There won’t always be a diagram given to you!
F = 8 (2 hexagons + 6 rectangles)
E = ???
2 hexagons have 6 edges each (12)
6 rectangles have 4 edges each (24)
That’s “36” edges, but each edge is SHARED by 2 faces so ÷ by 2…
E = 18

5. Euler’s Formula F + V = E + 2 8 + V = 18 + 2 V = 12
F = # of faces
V = # of vertices
E = # of edges
8 + V =
V = 12
Assignment: Page 514 #1 – 9, 13 – 18