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Parallelepiped

parallelepiped
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.
parallelepiped
How can you 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.
 
parallelepiped
To understand this shape, we just need to think of a regular brick.

Types of parallelepipeds

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

parallelepiped
parallelepiped oblique

How to make a rectangular parallelepiped?

net parallelepiped
net parallelepiped

To assemble the parallelepiped, you will need to print the shape net on a regular A4 sheet. Download the shape net here.
You can use either white and colored paper.

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

Download the shape net here.

1. Cut out the parallelepiped net along the marked lines.parallelepiped net
2. Glue the flaps according to their number sequence.
After gluing the central flap, we get:parallelepiped net
3. Glue the flaps along number 2 and number 3    parallelepiped
4. Now we have the finished model of a rectangular parallelepiped:parallelepiped
 

Rectangular parallelepiped shape nets

parallelepiped
net parallelepiped

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

 

parallelepiped
net parallelepiped

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

parallelepiped
net parallelepiped

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

parallelepiped
The aspect ratio of the parallelepipeds for the presented nets.

Oblique parallelepiped shape nets

parallelepiped oblique
net parallelepiped oblique

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 °

 

parallelepiped oblique
net parallelepiped oblique

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 remembering the names

There are cases when the word parallelepiped is confused with the word parallelogram.
And, indeed, these words are very similar.
 
So 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, hoever, 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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