**Quck answer**

A rhombicosidodecahedron is a polyhedron with 62 faces, including 20 equilateral triangles, 30 squares, and 12 regular pentagons. It has 60 vertices and 120 edges. This geometric shape is one of the Archimedean solids and is considered a semi-regular convex polyhedron. The name “rhombicosidodecahedron” comes from the combination of the words “rhombic” (referring to the rhombus-shaped faces) and “icosidodecahedron” (referring to its relationship to the regular icosidodecahedron). It has many interesting properties and is often used in mathematics and geometry for its unique characteristics.

Do you enjoy creating art? It’s a lot of fun! Many individuals like to sketch and color images. It’s also thrilling to experiment with various types of paint in art class. Some individuals prefer working with art materials using their hands. These individuals often prefer to create sculptures.

If you have ever used clay or Playdough, you understand how enjoyable sculpture can be. People can transform a lump of clay into anything they can imagine! At times, sculptors take on challenging projects. They might chip away at a rock to create monuments like Mount Rushmore. Others sculpt with ice. Sometimes, they make their artwork move, such as in kinetic sculpture. Many sculptors even utilize mathematics to shape their works of art.

Wait, mathematics? That’s correct! Many people may not be aware, but there is a strong connection between mathematics and art. Specifically, many sculptors use geometry in their work. They require knowledge of lines, shapes, and angles to bring their ideas to life.

Some geometric shapes are more difficult to sculpt than others. Most people could shape clay into the form of a sphere. A cube or pyramid may be slightly more challenging. Occasionally, artists challenge themselves by attempting to create very complex shapes. This was common during the Renaissance. It was also a popular theme in much 20th-century art. One particularly challenging geometric shape to sculpt is the rhombicosidodecahedron (pronounced “rom-bee-i-co-see-doe-dec-a-he- dron”).

Wow, that is a long word! It is also a very large shape. The rhombicosidodecahedron is a polyhedron. That is a 3D solid made up of flat shapes. A rhombicosidodecahedron is composed of 20 triangles, 30 squares, and 12 pentagons. It is a special type of polyhedron known as an Archimedean solid. This means that the sides of every triangle, square, and pentagon are of equal length. The rhombicosidodecahedron is one of only 13 Archimedean solids.

Are you struggling to visualize this structure in your mind? Start with a pentagon. Remember, that is a five-sided shape. Now, imagine a square connected to each side of the pentagon. In the space between each square, add a triangle. Next, attach a pentagon to the open side of each square. Repeat these steps, and you will end up with a rhombicosidodecahedron.

Is it still challenging to picture this shape? That is okay! It is one of the most complicated figures in geometry. That is what makes it exciting for sculptors to create. It is a great challenge! During the Renaissance, many artists also regarded the rhombicosidodecahedron as a religious and philosophical symbol. Some used the Archimedean solids to represent our solar system.

Would you like to attempt making a rhombicosidodecahedron? It may take a few tries to get it right! What other shapes would you try?

## Try It Out

Find an adult friend or family member to assist you with these activities:

# Explore Geometric Shapes

Have you ever tried creating your own rhombicosidodecahedron? If not, give it a try using the instructions provided. Once you’re done, take a look at your model and see how it turned out. You can also experiment with other shapes and see what you can create!

Geometric shapes are not just limited to art, they can be found all around you! Ask a friend or family member to help you identify shapes in your home or school. Make a list of objects and their corresponding shapes. Which shapes do you come across most frequently? Can they inspire any art projects?

Interested in learning more about Archimedean solids? Take some time to read about them. What new information did you discover? How does the rhombicosidodecahedron compare to other shapes? Write a paragraph summarizing your findings and share it with a friend or family member.

### Wonder Sources

- https://www.complang.tuwien.ac.at/schani/supermag/archimedean/index.html (accessed 21 May 2019)
- https://www.sacred-geometry.es/?q=en/content/archimedean-solids (accessed 21 May 2019)
- https://www.georgehart.com/virtual-polyhedra/archimedean-info.html
- https://www.georgehart.com/virtual-polyhedra/art.html (accessed 21 May 2019)
- https://www.georgehart.com/virtual-polyhedra/kepler.html (accessed 21 May 2019)

## FAQ

**1. What is a Rhombicosidodecahedron?**

A Rhombicosidodecahedron is a polyhedron with 62 faces, consisting of 20 equilateral triangles, 30 squares, and 12 regular pentagons. It is a convex polyhedron and one of the Archimedean solids. The name “Rhombicosidodecahedron” is derived from the Greek words for “rhombus,” “twenty,” “isosceles triangle,” and “twelve-sided figure.”

**2. How many vertices does a Rhombicosidodecahedron have?**

A Rhombicosidodecahedron has 60 vertices. Each vertex is where three or more edges meet. The vertices of a Rhombicosidodecahedron are formed by the intersection of the triangles, squares, and pentagons that make up its faces.

**3. What are the properties of a Rhombicosidodecahedron?**

A Rhombicosidodecahedron has several unique properties. It is a dual of the truncated icosidodecahedron, meaning that the positions of the faces and vertices are swapped. It also has rotational symmetry of order 2, meaning that it looks the same when rotated by 180 degrees around its center. Additionally, the angles between the faces of a Rhombicosidodecahedron are all equal, making it an isohedral polyhedron.

**4. How do you calculate the surface area of a Rhombicosidodecahedron?**

To calculate the surface area of a Rhombicosidodecahedron, you need to know the length of its edges. The formula for the surface area of a Rhombicosidodecahedron is A = 5√3a², where A is the surface area and a is the length of an edge. By substituting the value of a into the formula, you can find the surface area of the Rhombicosidodecahedron.

**5. Can a Rhombicosidodecahedron be constructed in the real world?**

While a Rhombicosidodecahedron is a mathematically defined polyhedron, it is not a common shape found in everyday objects. It can be constructed in the real world using various materials, such as paper or plastic, by following specific instructions and assembling the individual faces. However, due to its complex structure, constructing a Rhombicosidodecahedron may require advanced mathematical and spatial skills.

**6. What are some real-life examples of a Rhombicosidodecahedron?**

Although not commonly found, a Rhombicosidodecahedron can be seen in some architectural structures and sculptures. For example, the Buckminster Fuller Institute in the United States features a geodesic dome that resembles a Rhombicosidodecahedron. Additionally, some artwork and jewelry designs may be inspired by the geometric shape of a Rhombicosidodecahedron.

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