Tetrahedron is the simplest figure from polygons. It consists of four faces, each of which is an equilateral triangle, with each side being connected to the other by only one face. When studying the properties of this three-dimensional geometric figure for clarity, it is best to make a tetrahedron model of paper.
How to glue a tetrahedron from paper?
To construct a simple tetrahedron from paper, we need:
- actual paper (dense, you can use cardboard);
- protractor;
- ruler;
- scissors;
- glue;
- tetrahedron of paper, diagram.
Progress
- We begin work on the tetrahedron by drawing a sweep of paper. If the figure is planned from plain paper, you can draw a sweep directly on it.
- We draw a line that is the face of the tetrahedron. From two ends, we lay aside angles of 60 ⁰, and through the points obtained, draw straight lines until they intersect. We have an equilateral triangle.
- Next on each side of the triangle we construct the same. From each end we again postpone 60 ⁰ and connect. As a result, you should get a scheme consisting of four equilateral triangles.
- In order for the reamer to be glued together and to obtain a tetrahedron, one should make 1 cm allowances on three sides of different triangles. The result is this drawing.
- Cut out the scan and bend it along all the lines, let's bend the allowances inwards, if necessary, cut the corners. We glue them with glue and press them to the inner sides of the faces, joining the fold line between the side and the allowance with the side of the free triangle.
Some additional recommendations:
- if the paper is very dense, then in places of folds, you should hold a solid object, for example, the edge of the ruler;
- in order to get a multi-colored tetrahedron, you can paint the faces or perform a sweep on the sheets of colored paper.
How to make a tetrahedron from paper without gluing?
We bring to your attention a master class in which it is told how to assemble 6 tetrahedrons from paper into a single module using the origami technique.
We need:
- 5 pairs of square sheets of paper of different colors;
- scissors.
Progress
- Each sheet of paper is divided into three equal parts, cut and get the bands whose aspect ratio is 1 to 3. As a result, we get 30 bands, from which we will add the module.
- We put the strip in front of us face down, stretching horizontally. We fold in half, unfold and bend to the middle of the edge.
- On the far right edge, bend the corner so as to make an arrow, moving it 2-3 cm from the edge.
- Similarly, bend the left corner (photo as a paper to make a tetrahedron 3).
- We bend the right upper corner of the small triangle, which turned out as a result of the previous operation. Thus, the sides of the folded edge will be at the same angle.
- Expand the resulting fold.
- Expand the left corner and on the already existing fold lines wrap the corner inwards as shown in the photo.
- In the right corner, bend the top edge downwards so that it intersects with the fold made during operation # 3.
- The outer edge is wrapped again to the right using a fold made as a result of operation number 3.
- The previous operations are repeated from the other end of the strip, but so that small creases appear on the parallel ends of the strip.
- The resulting strip is folded in half along the length and let it mute uncover spontaneously. The exact angle of disclosure will become clear later, when the model is finally assembled. The element is ready, now we do 29 more in the same way.
- The link is inverted so that during its assembly its external side is visible. We connect the two links by inserting the tab into the pocket formed by a small internal angle.
- The united links must form an angle of 60 ⁰, under which other links will join (photo as of making paper tetrahedron 13).
- We add the third link to the second, and the second link to the first. The end of the figure is obtained, at the top of which all three of its links are connected.
- Similarly, add three more links. The first tetrahedron is ready.
- The angles of the finished figure may not be exactly the same, so for a more accurate fit, one should leave open the individual angles of all subsequent tetrahedra.
- Between themselves tetrahedrons should be connected so that the angle of one passes through the hole in the other.
- Three tetrahedra connected together.
- Four tetrahedra connected together.
- A module of five tetrahedrons is ready.
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If you have coped with the tetrahedron, you can continue and make a prism , icosahedron , parallelepiped and other geometric figures from paper .