1.
Summary of Polyhedral SolidsPolyhedral Solids
Prism
Pyramid
ExerciseExercise
Projection of Polyhedral Solids
2.
2
Summary of Polyhedral Solids
Prisms
Intersection lines of edge planes are called edge lines. IntersectionIntersection lines of edge planes are called edge lines. Intersection
lines of edge planes and bases are called base edge lines. Whenlines of edge planes and bases are called base edge lines. When
drawing projections of polyhedral solids, we are actually drawingdrawing projections of polyhedral solids, we are actually drawing
the projections of all edge lines and base edge lines followedthe projections of all edge lines and base edge lines followed
by a visibility test of the projected edge lines and base edge lines.by a visibility test of the projected edge lines and base edge lines.
Pyramids
Polyhedral solids
Polyhedral solids: The solids that are surrounded by planes are
called polyhedral solids.
3.
3
Class by theClass by the bases ofbases of prismsprisms
TriangularTriangular prismprism
PrismPrism
Square prismSquare prism PentagonalPentagonal prismprism HexagonalHexagonal prismprism
Draw stepsDraw steps Draw centerlines andDraw centerlines and datumdatum lines.lines.
Add lines for the upper and lower (end) faces.Add lines for the upper and lower (end) faces.
Complete three views.Complete three views.
Projection of pentagonal prism
1. Projection of a prism1. Projection of a prism
…………
4.
4
Example3. Draw the pentagonal prism and get points on the surface.Example3. Draw the pentagonal prism and get points on the surface.
The projection of point is not visible when it is on invisible edge or plane.The projection of point is not visible when it is on invisible edge or plane.
IdentificationIdentification
The projection of point is also visible when it is on visible edge or plane.The projection of point is also visible when it is on visible edge or plane.
MethodMethod
Getting points on surfaces of a prism can be based on the accumulationGetting points on surfaces of a prism can be based on the accumulation
characteristics of edge lines or plane projection.characteristics of edge lines or plane projection.
2.2.Getting points on the surface of a prismGetting points on the surface of a prism
LabelingLabeling All invisible points are written in brackets.All invisible points are written in brackets.
Example1. Draw the triangular prism and get points on the surface.Example1. Draw the triangular prism and get points on the surface.
Example2. Draw the square prism and get points on the surface.Example2. Draw the square prism and get points on the surface.
PrismPrism
5.
5
Class by theClass by the bases of a pyramidbases of a pyramid
TriangularTriangular pyramidpyramid
1. Projection of pyramid1. Projection of pyramid
SquareSquare pyramidpyramid PentagonalPentagonal pyramidpyramid Hexagonal pyramidHexagonal pyramid
Draw stepsDraw steps
1.Draw symmetry lines and the base of the pyramid.1.Draw symmetry lines and the base of the pyramid.
2.Add the vertex of the pyramid.2.Add the vertex of the pyramid.
3.Complete three views after adding lines for the side faces.3.Complete three views after adding lines for the side faces.
Pyramid
…………
6.
6
2.2.Getting points on the surface of a pyramidGetting points on the surface of a pyramid
AA
KK
C
B
P
E
F
Draw an auxiliary lineDraw an auxiliary line or planeor plane going through the point on the pyramid.going through the point on the pyramid.
DistinguishDistinguish
LabelingLabeling All invisible points are written in brackets.All invisible points are written in brackets.
Example4. Draw a regular triangular pyramid and get points on theExample4. Draw a regular triangular pyramid and get points on the
surface.surface.
Example5. Draw a regular pentagonal pyramid and get points on theExample5. Draw a regular pentagonal pyramid and get points on the
surfacesurface..
Pyramid
The projection of point is also visible when it on visible edge or plane.The projection of point is also visible when it on visible edge or plane.
The projection of point is not visible when it on invisible edge or plane.The projection of point is not visible when it on invisible edge or plane.
MethodMethod
7.
7
a"
Exercise.. Complete each drawing by adding the missing detail.Complete each drawing by adding the missing detail.
（（ 11 ）） Draw a prism and get points on the surface.Draw a prism and get points on the surface.
c'
a'
(b')
a
a"
b
(c")
c
b"
（（ 22 ）） Draw a pyramid and get points on the surfaceDraw a pyramid and get points on the surface
a b
c
a'
b'
c"(c')
(b")
9.
9
Example1Example1.. Draw the triangular prism and get points on the surface.Draw the triangular prism and get points on the surface.
( b)
a
A
B
S
Draw view of the end faces.Draw view of the end faces.
Complete three views.Complete three views.
Draw all views of points.Draw all views of points.
Steps
a"a'
(b' ) b"
10.
10
d"
c
d
C
D
S
Example2. Draw the square prism and get points on the surface.Example2. Draw the square prism and get points on the surface.
Draw view of the end faces.Draw view of the end faces.
Complete three views.Complete three views.
Draw all views of points.Draw all views of points.
Steps
c"
d'
（ c")
11.
11
F
E
S
Example3. Draw the pentagonal prism and get points on the surface.Example3. Draw the pentagonal prism and get points on the surface.
Steps
（（ 11 ）） DrawDraw thethe accumulation topaccumulation top
view.view.
（（ 22 ）） DrawDraw thethe limit elements.limit elements.
（（ 33 ）） Draw all views of prism.Draw all views of prism.
（（ 44 ）） Draw all views of points.Draw all views of points.
e' e"
（ f")f'
f
e
12.
12
a' c'
b'
Steps
a c
b
k
1＇
1
K
C
A
B
S
Example4. Draw a regular triangular pyramid and get points on theExample4. Draw a regular triangular pyramid and get points on the
surface.surface.
（（ 11 ）） DrawDraw thethe top view.top view.
（（ 22 ）） DrawDraw thethe limit elements.limit elements.
（（ 33 ）） Draw all views ofDraw all views of pyramidpyramid ..
（（ 44 ）） Draw all views of pointDraw all views of point DD.. （（ 55 ）） Draw all views of pointDraw all views of point EE..
P E
D
a"(c") b"
d' （ d")
e' e"
e
d
k"k'
p'
p
13.
13
Example5. Draw a regular pentagonal pyramid and get points onExample5. Draw a regular pentagonal pyramid and get points on
the surface.the surface.
D
E
A
B
C
K
b k d
a e
c
F
G
S
f
Steps
11 ）） DrawDraw the topthe top
view.view.
22 ）） DrawDraw thethe limit elements.limit elements.
33 ）） Draw all views ofDraw all views of pyramid.pyramid.
44 ）） Draw all views of pointDraw all views of point GG.. 55 ）） Draw all views of pointDraw all views of point F.F.
g'
g"
（ f")f'
g
b' (a') c' (e') d' a"(e") b"(d") c"
k"k'
p'
p
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