Warm-up
Name the following polygons.
3 side
4 sides
5 sides
6 sides
7 sides
8 sides
9 sides
10 sides
12 sides
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
dodecagon
 Three Dimensional figures that have length, width and
height
 A solid formed by polygons that enclose a single region
of space.
Face: flat polygonal surface of a polyhedron.
Which figure below is not a polyhedron? Why?
a)
b)
c)
d)
1)
Polyhedrons are classified by the number of faces.
2) What is the minimum number of faces a polyhedron
could have?
a) 2
b) 3
c) 4
d) 5
Tetrahedron
Pentahedron
 6 sides
 Hexahedron
 7 sides
 Heptahedron
 8 sides
 Octahedron
 10 side
 Decahedron
 12 sides
 Dodecahedron
Regular Polyhedron
A polyhedron whose faces are
congruent regular polygons.
3) Which polyhedron below is
regular?
a)
b)
c)
- A polyhedron with two face that are congruent and
parallel polygons and whose other faces are
parallelograms formed by segments connecting
the corresponding vertices of the bases
Bases: the two polygonal faces that are both congruent
and parallel in a prism
Lateral faces: the faces that are not the bases, but the
sides that are parallelograms in a prism
Base
Lateral
face
Lateral face
Base
Prisms are named for their bases
What kind of prism is displayed above?
Hexagonal Prism
Name the Prisms below:
1)
1)
Triangular Prism
2)
2) Rectangular Prism
3)
3)
Pentagonal Prism
 A polyhedron where one face is a polygon(the base)
and the other faces (lateral faces) are triangles that
meet at a common point called the vertex.
 Pyramid is named after the polygon that is the base
Lateral face
base
1)
1)
Rectangular Pyramid
2)
2) Triangular Pyramid
3)
3)
Hexagonal Pyramid
1)
Rectangular
Pyramid
Pentahedron
2)
3)
Heptahedron
Pentagonal Prism
Cube
Rectangular
Prism
Hexahedron
 The set of all points in space at a given distance from a
given point called the center
 A three dimensional figure with two congruent
circular bases that lie in parallel planes
 A three dimensional figure that has a circular base, a
vertex not in the plane of the base and a curved lateral
surface.
Edges:
line segments where the faces intersect.
Vertex: point of intersection of three or more edges.
vertex
Edge
Fill in the table below to find a relationship between Faces,
Vertices and edges of Polyhedra
Polyhedron
Faces
Vertices
Edges
4
4
6
8
12
5
5
8
7
10
6
15
Euler’s Formula
(oy-ler)
Face + Vertices = Edges + 2
1) How many edges does a polyhedron with 20 faces and 12
vertices have ?
20 + 12 = E + 2
E= 30
2) How many vertices does a figure with 5 faces and 9 edges have?
5 + V = 9+ 2
V= 6
3) Haw many faces does a figure with 6 vertices and 12 edges have?
F + 6 = 12+ 2
F= 8
4) How many vertices does a figure with 20 faces that are all
triangles have?
20 + V = E + 2
E= (F●sides)/2
V= 12
CLOSURE
EXIT TICKET: Write down Euler’s Theorem and state
what each letter stands for.
HOMEWORK
pg. 723 #6-18, 47-49 all