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Archimedean Polyhedra. How to make pdf template

Archimedes, a scientist from Ancient Greece, discovered thirteen types of polyhedra, now called Archimedean solids, referred to as semi-regular polyhedra.

Each of them is limited by different polygons where the polyhedral angles and identical polygons are equal. Furthermore, the same number of equal faces meet at each vertex. In the same order, each of these solids can be inscribed into a sphere.
All these thirteen names make your head spin when you see them for the first time. However, it is possible to sort things out, understand, and remember them.

What all Archimedean solids look like

1. Truncated tetrahedron

2. Truncated octahedron

3. Truncated hexahedron (or truncated cube)

4. Truncated dodecahedron

5. Truncated icosahedron

6. Cuboctahedron

7. Rhombicuboctahedron

8. Truncated cuboctahedron

9. Snub cube

10. Icosidodecahedron

11. Truncated icosidodecahedron (Small rhombicosidodecahedron)

12. Truncated rhombicosidodecahedron

13. Snub dodecahedron

How is the name of the polyhedron formed?

Pay attention to the fact that there is a word-basis for every type of polyhedron which forms their names. It is this word-basis that helps to classify the current polyhedra to one of the five regular polyhedra.

Name	Word-basis
Truncated tetrahedron	tetrahedron
Truncated octahedron Cuboctahedron Rhombicuboctahedron Truncated cuboctahedron	octahedron
Truncated cube Snub cube	cube
Truncated dodecahedron Icosidodecahedron Truncated icosidodecahedron Truncated rhombicosidodecahedron Snub dodecahedron	dodecahedron
Truncated icosahedron	icosahedron

Which polyhedra forms the basis?

One of the five Platonic polyhedra forms the basis for these 13 types of polyhedra.

What can geometric figures be used to construct the Archimedean polyhedra?

All types of Archimedean polyhedra can consist of a certain set of regulars.

1. Truncated tetrahedron : 4 triangles + 4 hexagons

= 4

+ 4

2. Truncated octahedron: 6 squares + 8 hexagons

= 6

+ 8

3. Truncated hexahedron (or truncated cube): 8 triangles + 6 octagons

= 8

+ 6

4. Truncated dodecahedron: 20 triangles + 12 decagon

= 20

+ 12

5. Truncated icosahedron: 12 pentagons + 20 hexagons

= 12

+ 20

6. Cuboctahedron: 8 triangles + 6 squares

= 8

+ 6

7. Rhombicuboctahedron: 8 triangles + 18 squares

= 8

+ 18

8. Truncated cuboctahedron: 12 squares + 8 hexagons + 6 octagons

= 12

+ 8

+ 6

9. Snub cube: 32 triangles + 6 squares

= 32

+ 6

10. Icosidodecahedron: 20 triangles + 12 pentagons

= 20

+ 12

11. Truncated icosidodecahedron: 20 triangles + 30 squares + 12 pentagons

= 20

+ 30

+ 12

12. Truncated rhombicosidodecahedron: 30 squares + 20 hexagons + 12 decagons

= 30

+ 20

+ 12

13. Snub dodecahedron: 80 triangles + 12 pentagons

= 80

+ 12

The size of a polyhedra

To create a polyhedra collection, we need to adhere to certain conditions so that sizes will be comparable and models can easily be compared with each other.
One of the options is to create a model that fits into the sphere of the standard sizes. Then all 13 polyhedra will look like this:

Another option is to set up the same length for the side of all the polygons, which will be used in the model. The proportion of polygons with the same side length is:

- Triangle;

- Square;

- Pentagon;

- Hexagon;

- Octagon;

- Decagon.

This is what the collection of polyhedra with the same side length will look like:

All arhimedеan solids in Magic Edges sets.

Where to find the nets of Archimedean solids

Nets for all thirteen Archimedes polyhedra can be found in the kit "Magic Edges":

Magic Edges № 18
- Truncated tetrahedron;
- Truncated octahedron;
- Truncated cube;
- Cuboctahedron.

Magic Edges № 19
- Truncated icosahedron;
- Icosidodecahedron;
_
_

Magic Edges № 21
- Rhombicuboctahedron;
- Truncated cuboctahedron

Magic Edges № 27
- Truncated dodecahedron;
- Small rhombicosidodecahedron

Magic Edges № 29
- Snub cube;
- Snub dodecahedron

Magic Edges № 31
- Truncated icosidodecahedron toroid;
-

Archimedean Polyhedra. How to make pdf template

Archimedes, a scientist from Ancient Greece, discovered thirteen types of polyhedra, now called Archimedean solids, referred to as semi-regular polyhedra.

What all Archimedean solids look like

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