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polyhedron
a three-dimensional figure
whose surfaces are polygons
faces
edge
vertex
Euler’s Formula
The number of faces (F), vertices (V), and
edges (E) of a polyhedron three-dimensional are
related by the formula
F + V = E + 2
Example
A polyhedron has 8 faces and 18 edges. How many vertices
does this polyhedron have ?
F + V = E + 28 + V = 18 + 28 + V = 20-8 -8
V = 12
Euler’s Formula
The number of faces (F), vertices (V), and
edges (E) of a polyhedron in two-
dimensional are related by the formula
F + V = E + 1
How many regions, vertices and
segments are on the following polyhedron in 2-dimension space
?
regions
1
2
3
4
5
6
7
8 8
segments
1
2
3
4
5
6
7
8
9
10 11
12
13
14
15
16
17
18
19 20
21 22 23
24
25 26
2728 29
29
How many regions, vertices and
segments are on the following polyhedron in 2-dimension space
?
regions 8 segments
1
2
3
4
5 6
7
8
9
10 11
12
13
14
15
16 17
18
19
20 21 22
22
29
vertices
Cross sections
Slicing the polyhedron with a plane and examining the resulting figure.
AssignmentWorkbook
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