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Parallelepiped

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A parallelepiped is a polyhedron with six faces.
 
For a rectangular parallelepiped, all six faces are rectangles.
For an arbitrary parallelepiped, all six faces of the parallelogram.
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How to understand and remember the word parallelepiped?
Divide it into two parts:
           paralle - means parallel (Greek),
             pypid - means the plane (Greek).
Or a geometric body bounded by parallel planes.
 
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To understand what kind of a geometric solid, an ordinary brick is best suited.
This is a real rectangular box.

Types of parallelepipeds

All types of parallelepipeds can be divided into rectangular and oblique.

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parallelepiped oblique1 9

How to make a rectangular parallelepiped?

net parallelepiped 1 1
net parallelepiped 3 1

To assemble the parallelepiped, you will need to print the unfolding on a regular A4 sheet. Download the net.
For printing, you can use both white and colored paper.

If you are using a color printer, then we suggest making a parallelepiped where the parallel faces have the same colors.

Download the net.

1. Cut out the parallelepiped net along the marked lines.parallelepiped razvertkaf 1
2. On the flaps indicated sequence gluing.
Sticking central flap we get:parallelepipedf 2
3. Glue the parts in the gluing place number 2 and number 3    parallelepipedf 3
4. Get the finished model of a rectangular parallelepiped:parallelepipedf 4
 

Rectangular parallelepiped nets

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net parallelepiped 1 1

Download the net of a rectangular parallelepiped for printing on A4 sheet
 
Geometrical dimensions of the finished parallelepiped model (mm):
Length = 120
Width = 90
Height = 40

 

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net parallelepiped 1 2

Download the net of a rectangular parallelepiped for printing on A4 sheet
 
Geometrical dimensions of the finished parallelepiped model (mm):
Length = 90
Width = 65

Height = 50

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net parallelepiped 1 3

Download the net of a rectangular parallelepiped for printing on A4 sheet
 
Geometrical dimensions of the finished parallelepiped model (mm):
Length = 60
Width = 40
Height = 65

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The aspect ratio of the parallelepipeds for the presented nets.

Oblique parallelepiped nets

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net parallelepiped oblique2 1

1. A parallelepiped having a slope in one plane.
One pair of side faces is not perpendicular to the base.
 
Download the net of the inclined parallelepiped for printing on A4 sheet
 
Geometrical dimensions of the finished parallelepiped model (mm):
Length = 100
Width = 60
Height = 45
The angle of the side faces = 26.3 °

 

parallelepiped2 2
net parallelepiped oblique2 2

2. A parallelepiped having a slope in two planes.
Both pairs of side faces are not perpendicular to the base.
 
Download the net of the inclined parallelepiped for printing on A4 sheet
 
Geometrical dimensions of the finished parallelepiped model (mm):
Length = 105
Width = 80
Height = 43
Tilt angle of the 1st pair of side faces = 26.3 °
Tilt angle of the 2nd pair of side faces = 16 °

 

Difficulty memorizing

There are cases when the word parallelepiped is confused with the word parallelogram.
And, indeed, these words are consonant.
 
What is the difference between parallelepiped and parallelogram?
A parallelogram is a quadrangle whose opposite sides are parallel, that is, they lie on parallel straight lines. Special cases of the parallelogram are rectangle, square and rhombus.
A parallelogram is a flat figure.
A parallelepiped is a volume solid, all faces of which are parallelograms.
A parallelepiped is a polyhedron with six faces and a parallelogram each.

Joke:
"Sometimes, careless students try to calculate how many grams are in a parallelogram and how many parallel pypids are in a parallelepiped!"

 

 

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