How to assemble a rhombus from 8 parts. The pyramid is a sweep. Unfolded pyramid for gluing. Paper sweeps. Making different models of polyhedra
The rest of the blocks - scraped together on the bottom of the barrel.
Assembly - according to stencil patterns. This is explained by the fact that I have at my disposal a set of fabrics consisting of squares 25 cm X 25 cm (10 inches by 10 inches).
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BLOCK 1.STAR FROM DOMBS. THREE COLORS.
This star is widely known. In the English-speaking environment, she has some name such as "Star of Sarah Connor", "Star of Oklahoma" or "Star of the victory of 300 heroes on Blue Stone Mountain". I don’t think it necessary to search for this name and give it: it doesn’t mean anything to Russians.
(Found the name. Guessed it: "Star of Virginia"))))).
The drawing below is only needed if a block of a certain size is needed. (All this geometry allowed us to make only one, but an important conclusion: for the desired block size 36 X 36 cm, the length of the rhombus side is 5 cm. square).
Four types of fabric are needed:
"1" - an asterisk in the center, 8 rhombuses;
"2" - central part, 16 rhombuses;
"3" - acute angles of rays, 8 rhombuses;
background fabric.
Cutting from strips is possible: strip of fabric "1" + strip of fabric "2" (see pink element); fabric strip "2" + fabric strip "3" (see yellow element).
But I have fabric in sets: small squares. Only a cut from individual parts is possible. Alas!
Three types of rhombuses are prepared, and the yellow squares are filling the space between the corners of the star, the background fabric. There are 8 squares in total. Where the pattern requires triangles from the background fabric, it is better to sew in the squares, and then cut them off.
Insofar as rhombus is a very tricky part for connection, there are a number of required steps to follow.
1) On the seamy side of each rhombus, applying a pattern, mark the points of the corners with a pencil or marker.
The numbers are my cutting dimensions. Do not pay attention))).
2) Connecting individual rhombuses, pierce these points, and only then connect the parts with a pin for further sewing on a typewriter.
If you connect diamonds by eye, then the number of successful connections will be correlated with unsuccessful ones as 1: 5. Checked.
3) When connecting the already sewn parts, you need to pierce the seam place at the first and second parts through and through, retreating to the width of the allowance (red pin), and only then split the parts with pins for further work on the typewriter.
When connecting a star with squares from a background fabric, you need to: 1) connect each side separately (under no circumstances turn at corners!) and 2) bring the seam to the point on the diamond that was marked with a marker.
The assembly order is dictated by the logic and structure of the block.
1) Connect rhombuses from fabric "1" with rhombuses from fabric "2" - 8 parts; and diamonds from fabric "2" with diamonds from fabric "3" - also 8 parts;
2) connect the "petal" or "face" of the star - 8 times;
3) connect 2 "petals" each;
4) connect sewn 2 "petals" and 2 "petals", get a semi-star - 2 parts;
5) connect 2 semi-stars - you get a star;
6) Connect the star to the background fabric in any order.
A different order is possible, if you do not mind cutting the background fabric.
Seamy side.
When smoothing, simple and general rules apply: smooth the allowances from converging seams in different directions (here it is important when joining rhombuses), iron the allowances on a darker fabric (here the allowances from the background fabric are ironed on the dark details of the star).
Process the point in the center, where 8 corners converge, again according to the general rules: rip the stitches to the very point of connection, put a finger in this "bud" and twist it. The allowances will fit optimally and there will be no lump.
The star is ready-made. It is beautiful in any design: blue, yellow, red, multi-colored. Win-win block.
BLOCK 2. STAR OF 12 RAYS (8 + 4). JUNE Star.
Why "Star of June"? Because it was made in June. I don’t know the English name, and I don’t want to know.
Star under different lighting conditions.
The peculiarity of this and similar stars is that the distance between the vertices of the rays both horizontally, vertically and diagonally must be the same (the diagonal is highlighted by a line). The calculations are simple: 1st segment - leg of an equilateral right-angled triangle, 2nd segment - its hypotenuse, 3rd segment - leg again.
The selection of fabric is simple: the first pair (dark, light), the second pair (dark, light), one or two background fabrics. This version of the star has 2 background fabrics, although there is only one on the diagram on the Internet.
A quarter of the diagram drawn will serve as a pattern.
This star does not obey any methods of quick assembly. Only element-wise connection! The only thing that this star allows is the division of the block into 4 squares, which are collected at the very end of sewing.
Parts are cut at different angles and, accordingly, are strongly deformed after sewing on a typewriter. The second square of the drawn diagram can serve as a pattern for trimming stitched elements.
Aligned items.
How to fold the allowances? With so many parts of different geometry, not all traditional rules apply. For example, a way to smooth out allowances only on the dark side is completely unthinkable.
The photo shows that the main desire was to bend the allowances in different directions, which is especially important when joining an angle-angle, when a thick seam is obtained.
Capricious star! To avoid distortions you need:
1) make large allowances up to 1 cm and even a little more, since the sewn elements need to be aligned during work;
2) mark the corners on the seamy side of each detail with a marker or pencil, and while stitching the parts, first pierce these points, and then split the parts with pins (all the details are different, the angles are different, there is nothing to focus on!).
But the harmony of the completed star will pay off.
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BLOCK 3. STAR WITH INTERLACED RAYS.
This star has no "volume", but there is another very interesting effect - the interweaving of details. That is why it is interesting.
In order for just such a pattern to form in the center, it is necessary that the parts of the side of the block correlate as follows: 3, 4, 3. For example, the side of the block is 30 cm, we carry out simple calculations: 30: 10 = 3 cm, 3 cm is the length of the conditional units; 3x3 = 9 cm, 3x4 = 12 cm.This means that the side must be divided into segments of 9 cm, 12 cm, 9 cm.
In order for the pattern to form, it is necessary to select 8 fabrics + background fabric. And nothing else. (In 4 fabrics the block is inexpressive, in 2 it is even better, but boring).
The simplicity of the block lies in the fact that all parts are right-angled triangles. This means you do not need to align the elements while sewing. But this simplicity is deceiving.
First, all triangles are of different sizes. In the diagram above, the different triangles are marked with a red felt-tip pen; it can be seen that 7 types of different right-angled triangles are required.
From each fabric (except for the background), it is necessary to cut out 3 triangles: for 4 types of fabric - one set, for the remaining 4 - a different set (see the triangles in the center are different!).
And the mix of details is full of surprises. The triangles of the star are connected to each other only part of the side. These funny points are highlighted below.
(Of course, you can simplify the assembly by cutting the triangles into pieces, but this will not add beauty).
This puts forward a number of requirements for cutting and sewing:
1) to the seamy side of all triangles of the star (excluding corners) you need to put a triangle pattern and mark the corners with a pencil or marker; bring the connecting seams only to these points;
2) and on those triangles that are connected to the neighboring triangle with an incomplete side, apply the points of their connection; on my diagram, these are large purple, yellow, blue, light green, in the center - small red, lilac, orange, blue. Do not connect them by eye!
The assembly is not easy, it looks like a puzzle. One of the possible options:
Assembling each star gives the master a special mood. This one brings satisfaction from solving a complex geometric problem. And admiring it is like the joy of having an "A" in mathematics.
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BLOCK 4. STAR WITH SHARP RAYS.
The peculiarity of this star is its sharp rays. This is achieved simply: when drawing a sketch, you need to divide the side into 3 equal parts. (The previous star was divided into three parts with a ratio of 3: 4: 3. You can compare the proportions).
The difficulties of making this star are already visible in the figure: 1) very sharp corners of the triangles, 2) convergence of 16 (!!!) angles at one point.
When connecting the edges of the rays, it is better not to trust the eye. It is necessary, having previously drawn the points of the corners on the seamy side of the parts, first connect these points (see red round pins), and only then prick the pins for sewing on a typewriter.
It is better to overdo it, to be on the safe side, than to spend time and effort and end up with a dubious product.
Techniques, techniques that facilitate work, can be used when connecting corner squares (those with "butterflies").
Since at one point, as already mentioned, 16 corners converge, you do not need to continue the seam to the edge of the fabric, connecting the faces of the star. You should stop at the marker dot marked on the seamy side.
The photo shows that 8 corners already create a sufficient mess, a kind of "bunch" of allowances.
How do I smooth out the seams? The star itself suggests the only option. There are 16 corners in the center. You can straighten them by ripping the seams to the center and "twisting" the allowances to one side. And, having twisted the allowances of the edges, the remaining allowances should be smoothed out in the way where the edges are "pulled".
Here is such a star ... Sewing is not difficult. But you need to prepare for the imperfect convergence of 16 corners. The seam is so thick that the machine's foot jumps over and shifts the connection point.
I would call this star - intriguing ... She, like a cat, walks by itself, sews by itself, behaves as she likes.
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BLOCK 5. STAR WITH BROKEN FACES.
In order to draw a sketch of this plump star, you need to divide the side of the square into 4 equal segments.
And again you need to strain, what needs to be strained, and relax what needs to be relaxed: again 16 angles at one point!
The star looks complicated, but you only need 4 types of fabric + background (I have 2 background).
The triangles are different, the angles are different, and the already familiar procedure should be repeated: draw the patterns on the seamy side, paying special attention to the points that indicate the corners of the triangles.
No matter how tedious and difficult it is, it needs to be done. It can be seen here that when triangles with different angles are connected, allowances of different sizes come out beyond the border of the line to be sewn. They cannot be guided by when sewing. Therefore, you need to pierce the points of the corners of the triangles to be sewn. (yellow round pins), and then fix the details.
The assembly option is prompted by the asterisk itself: it is optimal to sew along the edges.
Then the squares-quarters.
The allowances need to be smoothed out in the same way as for the 4th star: rip the seams to the center, press the center, turning the allowances to one side, and then follow how the ray allowances lay. And they will lie either clockwise or counterclockwise.
This star is simple. Calm. It is very easy to gather and gives peace.
BLOCK 6. SWINGER.
Small resting block. It is good to sew when you are tired of calculations and difficulties. Simple simplicity.
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BLOCK 7. BANTIK WITH LONG RIBBONS.
Here is such a cute bow. The cut and fit are clear at a glance.
Let's say the side of the square is the basis of this block - a. Then you need:
1) 7 squares of light fabric with a side ( a + allowances);
2) 4 squares of dark fabric;
3) 3 large squares of light fabric;
4) 2 large squares of dark fabric;
5) 5 large squares of background fabric;
6) 6 squares from the background fabric;
7) 2 rectangles of background fabric with sides ( a+ allowances) and ( 2a+ allowances);
8) 2 rectangles of background fabric with sides ( a+ allowances) and ( 5a+ allowances).
(The rectangles from the background fabric can be replaced with squares, then point 6 will change. You will need 20 squares).
Large squares appear because of the possible cut in this case. You need to cut out large squares, superimpose them on top of each other, sew along the perimeter, and then cut along the diagonals. As a result, squares are obtained from two multi-colored triangles.
Then the squares need to be ironed and aligned. How do you calculate the side of a large square? The diagram shows that its side is: the diagonal of the desired square + 2 diagonals of the allowances + 1 cm for alignment.
It is better to slightly enlarge the side of this large square, and then trim off the excess, aligning the resulting two-color squares.
The assembly is very simple: sew the parts horizontally (or vertically), then sew the resulting stripes. The only awakening of the brain is when smoothing out the allowances: one strip - to the left, the next strip - to the right ...
Here's a bow. Unfortunately, the thought comes late: it was necessary to use three fabrics, then the "weaving of ribbons" would be more expressive.
(The geometry is slightly disturbed because there are allowances around the perimeter, which will then disappear).
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BLOCK 8. FOUR LOOS. Or: DOUBLE BOW.
In the original, the block looks like this (see below). Possible execution in 8 types of fabric - for each buttonhole its own set.
But I will sew according to this pattern: 2 identical loops + a dedicated middle.
The block diagram is based on a square. You need to prepare:
1) very dark fabric - 2 large squares;
2) dark fabric 1 - 1 large square;
3) dark fabric 1 - 6 small squares;
4) dark fabric 2 - 1 large square;
5) dark fabric 2 - 6 small squares;
6) light fabric 1 - 1 large square;
7) light fabric 1 - 4 small squares;
8) light fabric 2 - 1 large square;
9) light fabric 2 - 4 small squares;
10) background fabric - 2 large squares;
11) 4 small squares.
Large squares are used to save time when making two-color triangle squares. (See block 7 just above - there is a cut and calculation).
After working with large squares, the workpieces look like this:
The block is prepared for assembly on a typewriter.
Final block.
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BLOCK 9. STAR IN A CIRCLE.
Here is such a star. Calm, laconic, restrained. I just want to say - educated, intelligent. Indeed, nothing more. The virtue of simplicity. Intellectual star. From a good family. European.
The scheme is already familiar: the distances between all the rays of the star (both vertically and horizontally and diagonally) should be the same. That is: leg, hypotenuse, leg.
Fabrics: 3 + background (I have 2 backgrounds, triangles in the center).
Cut - according to the patterns of the details. The pattern can be part of a life-size diagram.
I did not see any methods of simplifying the cut. (But this does not mean that they do not exist).
All details must be executed in 4 copies, only large triangles (I have green ones) - 12 pcs.
The assembly of the block is arbitrary. For me - by sector. Each sector is an extension of the sides of the triangles in the center. There are 8 sectors in total, 4 of each type.
Build sectors with a dark background triangles in the center.
Assembly of sectors with a light triangle in the center.
Then collect 2 sectors.
By 4. And finally, the last seam and final assembly.
Seamy side. The location of the allowances is chaotic. But, however, not haphazard. The main desire was to distribute the allowances of the converging seams in different directions.
Here is such a star. A star for calm contemplation, reflection, attempts to ponder over the questions of the universe: what is a person, how long does it take for the light of distant stars to reach the Earth, where pair socks disappear after washing ...
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BLOCK 10. DUTCH ROSE.
The block diagram is complex and simple at the same time. On the one hand, all the segments inside the block are the same: both the sides of the squares and the sides of the rhombuses. On the other hand, it is difficult to calculate the circuit if you need a blocka certain size.
I failed because I forgot how to solve equations with a square root. Therefore, I simply cut diamonds and squares with a side of 5 cm.The size of the block in this case is as follows: 34 cm x 34 cm.If you plan to sew on stencils, then the side of the block must be divided into segments 5, 5, 7, 7, 5, 5 cm ... (You can sew without stencils, and without drawings, since the dimensions of all parts are known).
If the block size does not matter, then the calculations are simple: see the Pythagorean formula. It will help you calculate the length of the two center line segments of the side of the block (that is, the hypotenuse of a right triangle.
The acute angle of the rhombuses is 45 degrees.
Cut, on the contrary, gives joy, speed, lightness. Stripes, then details.
You need to cut out:
1) rhombs from light fabric - 12;
2) rhombuses from dark fabric - 12;
3) diamonds from a very dark or contrasting fabric - 8;
4) squares from the background fabric - 28 (or 8 and 20).
You will have to assemble the block in detail and sew each seam separately. Otherwise, it is impossible. Rather, you can, but by cutting the background squares.
With this kind of assembly, it makes no difference where to start. The choice fell on the work from the center.
This "Dutch rose" does not get tired of delighting with surprises: there are many points where the angles of 3, 5, 6 details converge. Therefore, you need to strive to smooth the allowances around these points in different directions.
So this is what you are, a scarlet flower!
Registration.
Registration home page shops are simple, restrained, laconic. The first thing that catches the eye is a sign that depicts boxes with puzzles.
After a couple of minutes, it changes and appears on the screen very profitable proposition.
It is very easy to navigate the site, in the upper left corner is located menu, which includes the main sections.
Range.
There are 2 types of original puzzles in the online store: Challenging Puzzle and IQ PUZZLE.
IQ PUZZLE- a series of 21 puzzles of varying difficulty. The figure can be assembled from 4-10 pieces. The cost of one copy is 250-300 rubles.
* Solving puzzles does not require professional knowledge and skills.
At the moment, there are only 16 species in the store, I suggest you familiarize yourself with them.
But I know about the existence of other puzzles, for some reason they are not yet available for sale.
Challenging Puzzle Series- a novelty of the store and at the moment the manufacturer has developed only 5 types of puzzles of this type.
If only one correct figure can be assembled from IQ PUZZLE parts, then as many as three different figures can be obtained from Challenging Puzzle puzzles, therefore the cost is an order of magnitude higher - 400 rubles.
Checkout.
If you have decided on the order, then send the selected items to the basket. When choosing a puzzle, you will be prompted to go directly to the basket, or continue your search.
Do not forget to carefully check the order, especially the quantity and total amount, if everything is correct, then hurry up to click on "place an order". A simple, standard form will appear in front of you, in which you must specify your full name, phone number for communication, e-mail, choose a delivery method, address, payment method.
Taking orders 24/7! Very convenient, isn't it? After registration on the site, the manager calls back and clarifies the order and other nuances.
Payment, delivery.
You can pay for the order using bank cards, or in cash upon receipt.
Residents of Moscow can independently pick up the parcel from the warehouse, other buyers can use the courier service or the Russian Post.
Have you noticed that the amount of courier delivery does not differ from the amount you need to pay if you choose Russian Post?
Carefully study the list of cities to which this applies.
Eh ... what a pity that my city was not on the list, so I had to issue my parcel through PR, which means that the delivery time increased by 2-3 days.
My order:
I received my parcel at the Russian Post office. It took her a week to get to my city.
Upon receipt, the puzzles were in a small cardboard box.
It contains 2 IQ Puzzle "Rhombus" and "Tree" ordered by me. Branded boxes the size of cards, so puzzles can always be taken with you and carried away by them a group of friends.
On the front side there is an image of the finished figure.
Boxes with puzzles are decorated in black and orange colors, the design is restrained, but not without a drop of positive! When opening the box on the top, inner edge, we see fancy emoticons that will make anyone smile in return.
The puzzles themselves are enclosed in zip-lock packages, in which I keep to this day, not a single detail will definitely be lost.
The puzzles I have chosen are of medium difficulty, they have 6 and 8 pieces of different shapes, which are made of durable, dense plastic in the same color scheme. The quality is high, the surface is smooth, when fully assembled, they stand up to each other - millimeter to millimeter, there is nothing to complain about.
If you accidentally scattered the contents of the bag (or the kids helped you in this matter), then on the back of the package you can peep from which puzzle which puzzle.
Also on the reverse side you can find the manufacturer's contacts and age restrictions 16+. But personally, I strongly disagree with him. Puzzles are great for developing logic, memory, so you can offer a child to assemble a figure. I think that such puzzles can be a great gift for schoolchildren for any occasion.
And now the most interesting thing, I'll tell you how I collected the figurines.
IQ Puzzle "Wood".
This puzzle consists of 6 pieces. I started with it, since there are fewer parts than in the second, so it seemed that I would assemble it faster.
The process itself is very exciting, I went through, rearranged, turned over the puzzles for about 30 minutes and everything was unsuccessful! And I even thought that maybe the wrong parts were put into my kit, I double-checked, compared them with the image on the box, everything is in place, nothing was confused. I decided to try again and after 20 minutes I collected it! I will show you two options, one of which is correct.
Both options are similar, but in the second, the lower right leaflet is convex and the picture changes, not coinciding with what is shown on the box.
You can also understand that this is not the correct option by looking at the edge, which is 3 ml. above, but as I already mentioned "the puzzles must match up to the millimeter."
Of course, I offered my young man to put the puzzle together, he did it much faster, after 15 minutes he showed me the finished figure. "Men ... logic is developed," I thought, but he could not cope with the second one, he did not have enough patience.
IQ Puzzle "Rhombus".
This puzzle has 8 pieces. It looks simple. I began to collect focusing on the corners. Sly! But in the end, I got completely dissimilar figures. With this puzzle, the brain had to really break!
After 40 minutes, I dumped it and the next day I offered it to my parents. My father sat for about an hour, proving to me that these details are definitely not from this figure. And all because the semblance of a rhombus turned out, but it was not a solid figure. I'll show you his options.
To be honest, in despair, I tried to find the answer to this puzzle on the Internet, but since it is one of the novelties, there were no answers.
The next day I decided to try again and this lesson sucked me in again, but now, an hour later, the correct option appeared!
I didn't enjoy this view for a long time, I quickly disassembled everything, I didn't want to remember how to put this or that part correctly, because I planned to try to reproduce it at a different time.
And now I will show you another option, which I came to a week later. The outline of a rhombus, but large gaps, which definitely should not be. But I was convinced that this puzzle is not just one time.
I brought both puzzles to the company of my friends, the evening at the training camp flew by unnoticed. The tree was collected quickly, but the rhombus did not submit to them. Friends took turns asking them to take my puzzles home.
Outcomes:
Convenient interface;
An interesting series of puzzles;
Affordable prices;
Promotions for the purchase of several puzzles;
Receiving orders 24/7;
Fast processing and delivery;
Cash payment upon receipt;
In order to assemble the figures, you do not need to have more than abilities, puzzles perfectly develop creative thinking, spatial imagination, train memory, concentrate attention. You can collect them, either alone or in a company.
IQ Puzzle will be a great gift for relatives, friends and colleagues, so I recommend that you look into the online store and order them soon!
Thank you all for your attention!
Rectangle, square, triangle, trapezoid and others are geometric shapes from the exact science section. A pyramid is a polyhedron. The base of this figure is a polygon, and the side faces are triangles with a common vertex, or trapeziums. For a complete presentation and study of any geometric object, models are made. They use a wide variety of materials from which the pyramid is made. The surface of a polyhedral figure, unfolded on a plane, is called its unfolding. The method of converting flat objects into volumetric polyhedrons and certain knowledge from geometry will help to create a layout. It is not easy to make sweeps out of paper or cardboard. You will need the ability to carry out drawings according to the specified dimensions.
Materials and fixtures
Modeling and execution of multifaceted volumetric geometric shapes is an interesting and exciting process. A large number of all kinds of layouts can be made from paper. For work you will need:
- paper or cardboard;
- scissors;
- pencil;
- ruler;
- compass;
- eraser;
- glue.
Parameter definition
First of all, let's define what the pyramid will be. The unfolding of this figure is the basis for making a volumetric figure. Getting the job done will require utmost precision. If the drawing is incorrect, it will be impossible to assemble the geometric figure. Let's say you need to make a layout with the correct
Any geometric body has certain properties. This figure has a base and its top is projected to its center. Selected as the base This condition determines the name. The side edges of the pyramid are triangles, the number of which depends on the polyhedron selected for the base. In this case, there will be three of them. It is also important to know the dimensions of all the constituent parts of which the pyramid will be composed. Paper sweeps are made in accordance with all the data of the geometric figure. The parameters of the future model are discussed in advance. The choice of the material used depends on these data.
How is the unfolding of the correct pyramid performed?
The basis of the model is a sheet of paper or cardboard. Work begins with a drawing of the pyramid. The figure is presented in an expanded form. The flat image on paper is in accordance with the pre-selected dimensions and parameters. has a regular polygon base, and its height passes through its center. We make a simple model for a start. In this case, it is a triangular pyramid. Determine the size of the selected shape.
To build a flat pattern of a pyramid, the base of which is a regular triangle, in the center of the sheet, using a ruler and a pencil, draw the base of the given dimensions. Next, to each of its sides we draw the side faces of the pyramid - triangles. Now we turn to their construction. The dimensions of the sides of the triangles of the lateral surface are measured with a compass. We put the leg of the compass at the top of the drawn base and make a notch. We repeat the action, moving to the next point of the triangle. The intersection resulting from such actions will define the vertices of the side faces of the pyramid. We connect them to the base. We get the drawing of the pyramid. For gluing the volumetric figure on the sides of the side faces, valves are provided. We finish drawing small trapezoids.
Assembling the layout
Cut out the completed drawing along the contour with scissors. Gently bend the flat pattern along all the lines. We fill the trapezium valves inside the figure in such a way that its edges close. We grease them with glue. After thirty minutes, the glue will dry. The volumetric figure is ready.
First, let's imagine what a geometric figure looks like, the layout of which will be made. The base of the selected pyramid is a quadrangle. The side ribs are triangles. For work, we use the same materials and devices as in the previous version. We carry out the drawing on paper with a pencil. In the center of the sheet, draw a quadrilateral with the selected parameters.
Divide each side of the base in half. We draw a perpendicular, which will be the height of the triangular face. With a solution of a compass equal to the length of the side face of the pyramid, we make notches on the perpendiculars, setting its leg to the top of the base. We connect both corners of one side of the base to the resulting point on the perpendicular. As a result, we get a square in the center of the drawing, on the edges of which triangles are drawn. To fix the model on the side faces, add auxiliary valves. A stripe of one centimeter wide is enough for secure fastening. The pyramid is ready for assembly.
The final stage of the layout
Cut out the resulting pattern along the contour. Bend the paper along the lines drawn. The collection of the volumetric figure is carried out by gluing. Grease the provided valves with glue and fix the resulting model.
Volumetric layouts of complex shapes
After completing a simple polyhedron model, you can move on to more complex geometric shapes. Unfolding a truncated pyramid is much more difficult to perform. Its bases are similar polyhedra. The side edges are trapezoids. The sequence of work will be the same as that in which a simple pyramid was made. The sweep will be more cumbersome. To complete the drawing, use a pencil, compasses and a ruler.
Building a drawing
The unfolding of the truncated pyramid is performed in several stages. The side face of the truncated pyramid is a trapezoid, and the bases are similar polyhedra. Let's say they are squares. On a sheet of paper, we draw a trapezoid drawing with the specified dimensions. Extend the sides of the resulting figure to the intersection. As a result, we get an isosceles triangle. We measure its side with a compass. On a separate sheet of paper we build which will be the measured distance.
The next stage is the construction of the side edges that the truncated pyramid has. The unfolding is performed inside the drawn circle. The lower base of the trapezoid is measured with a compass. On the circle, mark five points that connect the lines to its center. We get four isosceles triangles. We measure the side of the trapezoid drawn on a separate sheet with a compass. We postpone this distance on each side of the drawn triangles. We connect the resulting points. The side faces of the trapezoid are ready. It remains only to draw the upper and lower bases of the pyramid. In this case, these are similar polyhedra - squares. Draw the squares to the upper and lower bases of the first trapezoid. The drawing shows all the parts that the pyramid has. The reamer is almost ready. It remains only to draw the connecting flaps on the sides of the smaller square and one of the trapezoid faces.
Completion of the simulation
Before gluing the volumetric figure, the drawing is cut out along the contour with scissors. Next, the scan is carefully bent along the drawn lines. We fill the fixing valves inside the model. We grease them with glue and press them to the edges of the pyramid. Let the model dry.
Making different models of polyhedra
Making volumetric models of geometric shapes is an exciting experience. To master it thoroughly, you should start by performing the simplest sweeps. Gradually moving from simple crafts to more complex models, you can start creating the most intricate designs.
Rubik's Pyramid - This puzzle was reported in 1982 by Science and Life magazine. Then she was a novelty and the interest in her was theoretical: “Masha is good, but not ours,” like children's car tracks. Now the toy factories began to produce the pyramid in large quantities and there was a practical interest: buy bought, but how to assemble it?
The site already had a diagram. Let us recall what was said in the magazine.
The pyramid is a geometric body of a tetrahedron. Like a Rubik's cube, it consists of elements that, when the faces are rotated, can shuffle from face to face. The role of cubes here is played by small tetrahedrons, of which a large tetrahedron is composed. It has four tops (c), 6 edge elements, or elements at the base (o) and 6 middle elements located between them (m). Around any of the four axes, you can turn the "top", or "pyramid" —two tiers at once.
Having placed the tetrahedron with some face towards itself (facade), we denote the vertices in the same way as is customary for a Rubik's cube: B (top), P (right), L (left) and T (back).
The same letters denote turns - clockwise without a stroke, and with a stroke - against. The main movement in solving the puzzle is turning the pyramid, that is, the vertices, together with the middle layer.
The main operations for putting the pyramid in order were named: a universal operation of the type VLV'L '(PVP'V', PLP'L '), cyclically rearranging three elementary pyramids on two faces, and a circular permutation of three elements of one face: P' LPL 'clockwise and VL'V'L - opposite. There are enough of them to solve the puzzle.
Is there an assembly algorithm similar to the one cube assemblies Rubik? - readers ask.
We give the floor to the inventor of the "Moldavian pyramid" engineer A. A. Ordynts, who offers two ways to solve the puzzle.
FIRST METHOD
Alternate construction of pyramid faces. At the same time, no attention is paid to the destruction of the previously constructed face.
First step. First of all, all the tops v unfold in their places so that the colors of the sides coincide with the color of the sides of the corresponding middle element, and at the same time, diamonds are formed at each vertex on each side vm consisting of two triangles of the same color. Then the middle elements unfold m
(together with tops v
and edge elements o) so that on each side of the pyramid there are rhombuses vm
only one color (see 1.2). Three diamonds of the same color can be built only on a well-defined edge. To facilitate the search for this face, it is necessary to proceed from the fact that the color of this face will be the one that is not on the vertex opposite to this face.
Picture 1
Second phase. After placing one-color rhombuses on four faces, for further construction, it is necessary to master auxiliary operations (Fig. 1, 2):
a) transfer of the edge element from the base to the top B without disturbing the construction of rhombuses by the operation PVP'V ',
b) approach to the initial position of the edge element at vertex B with breaking of the rhombuses at vertex B by operation B or B '.
Stage three. The base is being built - the lower layer of the pyramid (Fig. 3a, 36). The dot denotes the side of the rib element, which has the same color as the under construction face located below. The edge element, which has the color of the edge being built, is brought to the initial position with the help of auxiliary operations, while the location of the rhombuses at the vertex B is allowed to be disturbed. Then, depending on the position of the colors of the sides of this edge element at the initial position, one of the operations 3a or 3b is applied (TV'T 'or L'VL). The same shading in the figures denotes triangles of the same color. The color of the unhatched triangles is irrelevant. The result of the stage: the base has been built - the lower layer, in which, both on the face facing downwards, and on the lateral sides of the base, all the triangles are in place.
Picture 2
Stage four. By turning the vertices B, the rhombuses at the vertex B are set in place, and the pyramid is turned downward with a face of a different color.
Fifth stage. Repeating the third step to create a new face. At the same time, one should not pay attention to the fact that the order of elements on a previously constructed face is violated.
If necessary, build the third face in the same way.In rare cases, you have to build the fourth face, and the pyramid will be assembled.
SECOND METHOD
Layer-by-layer construction. After building the bottom layer - the base - according to the first method (see the third stage) one of three possible positions will be obtained:
1. The two rib elements at the apex are in place in the unfolded position. The rest of the elements are correct. The pyramid is assembled by the process: (P'LPL ') (VL'V'L).
Figure 3
2. The three rib elements at the apex are out of place. When the vertex is rotated 120 °, they fall into place, however, the vertex and middle element are not rotated correctly. In this case, depending on the position, processes (P'V'P) B '(P'V'P) or (PVP') B (PVP ') apply.
The Rhombus Star block is one of the most beautiful "star" blocks. It can consist of only eight rhombuses or many rhombuses, but the principle of assembly will be general in all cases. In English-language sources, such a block is most often called "Lone Star".
The block "Star of rhombuses" can be sewn in two ways: simply by cutting and connecting the rhombuses one at a time, or using the "From stripes" technique. Our master class will tell you in detail how to sew a block "Star from rhombuses" with your own hands and teach you how to use stripes to compose other patterns.
Block "Star from rhombuses": preparation for work
How to sew a block "Star from rhombuses" with your own hands? We will tell you about the "stripe" technique, thanks to which it will be much easier to sew the "Star from rhombuses" block. The edges of the square block are squares and triangles, so that the shape of the star is as visible as possible, it is better to cut them out of fabric that differs from the main ones.If you want to sew a star from small pieces of fabric, you will need a diamond pattern with a sharp 45 degree angle.
For the stripe technique, it is necessary to cut strips of the same width. Depending on the color scheme of the block, you will need a different number of stripes of each color. When cutting rhombuses from stripes, you will have a few extra triangular parts that can be used for a product with the "Star of rhombuses" block or set aside for future projects.
We will show you how to sew a star from three rows of rhombuses, but the number of such rows may be different. In this case, the parts of the block are cut out of stripes that are sewn not from two, but from a larger number of colors.
So, let's sew the block "Star from rhombuses" with our own hands!
Cut open
For a block about 22x22 cm in size, you will need:
- 1 strip of green fabric 4 cm wide and 60 cm long
- 1 strip of yellow fabric 4 cm wide and 60 cm long
- 2 strips of white fabric, 4 cm wide and 60 cm long
- Fabric for 8 background squares 9-9 cm
Progress
Stitch green and white stripes and white and yellow stripes.
Press the seam allowances towards colored fabrics. Adjust the total width of the stripes to 6cm (3 for each color).
Cut diamonds from the strips, lining up the fabric, as shown in the photo. The straight side of the rhombus is 6cm. Four rhombuses should slope to one side, four to the other.
You will have eight rhombuses from each strip and three extra triangles.
Place the diamonds with green details in the center of the star, as shown in the photo.
Sew together a rhombus with a green part and a rhombus with a yellow part (one ray of a star). It is necessary to combine the place where the flowers meet in the diamonds (in the center of the diamonds) at the seam level, as shown in the photo. Chip or sweep the first pair, open it and check if it is properly docked. In the future, also chop or knock off each pair of parts.
Trim the details. Lay out the block of stitched beams.
Sew on two beams, make sure that the allowances are laid out in different directions. Check the alignment of colored elements.
Fold out the 4-piece block. Trim the details.
Attach the background squares to the star, check the size of the squares.
Divide the seams at the corners of the star 3-4 stitches. Sew the squares on one side first, stopping the stitching exactly at the open seam of the star.
Expand the piece and sew on the second side of the square. Iron.
Iron the allowances of the square, depending on the color scheme of the block, on the darker side.
Adjust the block to a square shape.
The block "Star from rhombuses" is ready! "
