Polytopia
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Adopt a Polyhedron!

Polyhedra are trapped as ideas in the realm of abstraction. Help us to free them by adopting a polyhedron, giving it a name and building a model.

There are so many polyhedra that mathematicians are overwhelmed by naming and taking care of all of them. Each polyhedron has an individual structure and therefore a unique character. And who decided that you have to be Pythagoras to name a mathematical object after yourself?

Adopt a polyhedron now and name it. You can also search for polyhedra if you know their number or their adoption-name: 

2907 polyhedra live here. Here they are:

free 1284
adopted 1623
realized 220
individualized 56

Frequently asked questions

How can I adopt a polyhedron?

You can choose a polyhedron from the matrix. Select your polyhedron by clicking on one of the black pixels. The green pixels are the polyhedra that have already been adopted, so you can look at them but not adopt them again. The black ones are free.

When you have clicked on a pixel, you will see a detailed view of the polyhedra. You can turn it around and look at it from all angles. If you and the polyhedron get along well and you decide to adopt it, you can click: Adopt me.

A new window pops up and you can sign up with your email address. We will send you a confirmation email. Go to your email-inbox and click on the link in the email.

Congratulations, you have adopted your very own mathematical object! Now you can give it a name. This can be your name or the name of your pet or a fantasy name. Try to come up with a name right away, your polyhedron will be very happy once it is named.

Realize your Polyhedron

In order to free the polyhedron from abstraction, it needs to take shape as a model. There are two options available. One possibility is to download the paper template below the polyhedron. You can cut it out and glue it together along the tabs. Here (Video is in production.) is a video to help you assemble the paper model.

Another possibility to make a model is via a 3D printer. The data can also be downloaded below the polyhedron. You may use an online 3D print service (We are looking for a sponsor for you.), and have it sent to your home.

Now your polyhedron has come to life! In order to prove that – you know that proofs are the bread and butter in mathematics – take a picture and upload it. Since the photo proof is visible for all users, we would like to ask you to make sure that the photo contains only the polyhedron and a rather neutral background. Quadratic pictures look best on our website.

Individualize your polyhedron

To add a little personality to your polyhedron you may build a creative model of it. There are no limits to your unique ideas, or the choice of material. Classical materials like wood, clay or cardboard are possible, but polyhedra are naturally keen to experiment and very happy if you build them out of more creative materials. Why not make a cheese polyhedron in contrast to the old cheese cube? If you have made an individual model, please also upload a picture.

What is a Polyhedron?

Polyhedra consist of vertices, straight edges, and flat faces. In our project, we focus on convex polyhedra. This means that all inner angles between two edges or two faces are less or equal to 180°. No cavities, holes or indentations are allowed. The word polyhedron comes from the combination of Greek words poly- (many) and -hedron (face).

Polyhedra are classical objects in geometry. The ancient philosopher Plato describes the class of regular polyhedra. Nowadays we call them Platonic solids. These bodies consist only of regular polyhedra, i.e. equilateral triangles, squares and equilateral pentagons. Euclid gave the first constructive proof of the completeness of that classification in his treatise Elements.

Up until today polyhedra and their higher-dimensional relatives, the polytopes are thoroughly investigated by mathematicians. You can find more information about polyhedra and their properties in the glossary.

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Is every polyhedron really unique?

Yes, all polyhedra are different from each other. No two are identical. If you adopt a polyhedron, it really is unique. The polyhedra fundamentally differ in their combinatorial type. This means that no two polyhedra have the same order of vertices, edges and polygons.

What does Realization of a polyhedron mean?

A polyhedron is labeled realized when a model has been built. This may be a paper model, that can be crafted from the paper template, or a 3D printed object. In order to prove the realization, you must upload a picture that you have taken of the model.

What does Individualization of a polyhedron mean?

To get to know your polyhedron a little better and add some personality, you may also individualize it. This means that you make another model out of a creative material of your choice. This could be wood, a sponge carved into the same form, a polyhedral marble-cake or a Plexiglas figure. It is easiest if you base the structure of your individualized model on the paper or 3D printed version in order to get the structure of the polyhedron right. Again, a picture proof is necessary.

Is the adoption of a polyhedron official?

Of course, mathematical objects do not belong to anyone. You can not register patents or sue someone who has stolen an idea for them. Similarly, the polyhedra in our project are free beings, like the stars in the universe, which you can also adopt but can not take home. So the adoption is solely authorized by everyone’s acceptance. The project is backed by the Collaborative Research Center 109. This is an association of mathematicians of the Technical University Berlin and Technical University Munich, attached is also the Freie Universität Berlin.