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Stellated octahedron (or compound of two tetrahedra). How to make pdf template

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A red pyramid passed through a white pyramid or vice versa. Or maybe it is a complex of pyramids directed in different directions. These figures are always a mystery.

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The presented image of this polyhedron illustrates exactly its second name - the compound of two tetrahedra. Here you can imagine a red tetrahedron pointing up through a beige tetrahedron that points down.

However, mathematicians prefer to call the polyhedron a stellated octahedron.

The stellated octahedron could be defined as a regular polyhedron since all its faces are regular triangles of the same size and all angles between them are equal.

But in fact, this geometric solid is not the sixth regular polyhedron on par with the five known Platonic solids. The reason is that the word convex is present in the definition of a regular polyhedron—that is, all faces must lie on one side of the plane passing through any of them.

History of its discovery

The star octahedron was first depicted in 1509 in a book De Divina proportione written by the mathematician Luca Pacioli (1445-1514) with illustrations from Leonardo da Vinci.
The stellated octahedron was made in the form of an interconnected eight-frame tetrahedron. Then, almost 100 years later, the polyhedron was rediscovered by Johann Kepler. The Stella octangula, the octagonal star, was named after him. It is this illustration of a stellate octahedron that adds controversy about how this polyhedron was discovered.

The first possible variant is to attach 8 tetrahedra to the octahedron's sides or to continue the planes parallel to the octahedron's sides, getting the same 8 tetrahedra at the intersection of the planes. In other words, create a star-shaped octahedron.

Second way: Combine two tetrahedrons that clearly illustrate the faces' color in two colors (red and beige).

Video. The rotation of a polyhedron

Video. The polyhedron transform

The polyhedron properties

stellated octahedron inscribed in a cube

2. Here, we see an interesting feature of the polyhedron. If all the pointed tops are interconnected, the intersection lines correspond exactly to the cube's edges. Thus, the stellated octahedron can be inscribed in a cube.

stellated octahedron and the star of david

3. If you look at the polyhedron from above or at the shadow cast, the pattern outlines will create a regular hexagonal star.
The hexagonal star in two intersecting triangles is the oldest symbol, referred to as the Star of David (another name is the Seal of King Solomon).
Also, there are esoteric interpretations of the properties of a polyhedron.

Pattern 1

Pattern 2

Pattern 3

Stellated octahedron from the set "Magic Edges"

To assemble a polyhedron, we provide you with ready-made nets that are pre-cut and folded.
To do this, you need to use the details of the kit from Magic Edges 15.
Also, in the release itself, you will find information about the structure of the polyhedron.
The rotation of the finished polyhedron. The polyhedron is assembled from the kit - "Magic edges 15".

Stellated octahedron (or compound of two tetrahedra). How to make pdf template

The stellated octahedron could be defined as a regular polyhedron since all its faces are regular triangles of the same size and all angles between them are equal.

History of its discovery

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