Among all the existing geometric shapes that appeared back in antiquity, the octahedron is considered one of the most interesting. This figure is one of five bodies called platonic. It is correct, symmetrical and multifaceted, and also has sacred significance in terms of the stereometry practiced in ancient Greece. Today, this geometric body is studied by children at school, and in order to understand its structure better, we will consider how to make an octahedron from paper.
We will prepare the materials
All that is needed during this process is scissors, glue, a pencil, a ruler, and the paper itself, which will form the basis of the future craft. It is believed that the independent production of such stereometric figures improves abstract thinking, allows you to better navigate in space. Therefore, with the help of our short lesson, you can make up for geometric skills missed at school or suggest that your child create something similar if he has problems with the perception of geometric spaces and shapes.
Sketch - a faithful helper
The first option on how to make an octahedron out of paper is a ready-made sketch. The article proposes a picture that depicts this figure in a scan, and all that remains for you is to print it and glue it along the outlined lines. So your craft will have the most accurate parameters. Do not forget to pre-stick paper on cardboard so that the octahedron is more durable and lasts longer. This is especially important if it is intended for a child.
Do it yourself
Another option for making an octahedron out of paper is based on simple formulas and plotting. This geometric figure consists of 8 faces, 6 vertices and 12 edges, each 4 of which converge at one vertex. If you add together all the angles of the octahedron, then the sum will be equal to 240 degrees. It is also worth noting that this mythical stereo image has a triangular base and is completely symmetrical, therefore it is often called an antiprism.
Stereometry lessons
The scan of the octahedron represents a certain set of triangles that are completely equal to each other. Six of them are arranged in a single row according to the “jack” principle, and the other two with their bases adjoin the two middle figures from different sides. Therefore, the answer to the question of how to make an octahedron out of paper without layouts is simple. You only need to select a single face value, and put it at the base of eight equilateral triangles. Do not forget to leave allowances on the fold line, along which you glue the future crafts.
Intricate Secrets of Geometry
There are various varieties of this stereo figure. Among these, it is worth mentioning the cuboctahedron. The scan consists of 6 squares and 8 regular triangles, which are assembled into a volumetric body according to the rules of symmetry. This figure is semi-correct, and, it is worth noting, quite young. It was discovered by the creator of Leonardo da Vinci, and was then called the "star-shaped octahedron." You can also do it according to the scheme proposed in the article.