Polyhedra in Natural Science

In this exhibition, we will see how polyhedra are used in chemistry, biology, and mathematics.

Even seemingly difficult scientific concepts can be friendly.

**The Polyhedron Science Lab**

Polyhedra in Natural Science

In this exhibition, we will see how polyhedra are used in chemistry, biology, and mathematics. Even seemingly difficult scientific concepts can be friendly.

**The Polyhedron** Science Lab

At the Polyhedron Science Lab, you can be a scientist to create your own polyhedra from block pieces. You can learn the self-assembly of matter, an important concept in science, through a fun and simple experience.

**Scientific Inspirations & Discoveries through Polyhedra
**

**The Polyhedron** Science Lab

At the Polyhedron Science Lab, you can be a scientist to create your own polyhedra from block pieces. You can learn the self-assembly of matter, an important concept in science, through a fun and simple experience.

Scientific Inspirations & Discoveries

through Polyhedra

nspired by the geodesic dome, designed for stability and efficiency,

Watson and Creek hypothesized that a virus known

as a ball is actually a polyhedron.

Later it turned out to be an icosahedron.

This is a result of synergy between science and

art, showing the importance of convergent thinking.

**Soccer Ball made by Scientists**

**Scientific Inspirations & Discoveries**

through Polyhedra

Inspired by the geodesic dome, designed for stability and efficiency, Watson and Creek hypothesized that a virus known as a ball is actually a polyhedron. Later it turned out to be an icosahedron. This is a result of synergy between science and art, showing the importance of convergent thinking.

**Soccer Ball made by Scientists**

Kroto, Curl, and Smalley, who won the Nobel Prize in Chemistry in 1996, discovered Buckminsterfullerene, C60. They found that 60 carbon atoms are arranged like a soccer ball. Fullerenes have the shape of a truncated dodecahedron, consisting of 12 pentagons and 20 hexagons, and the pentagons are surrounded by hexagons. Fullerene is a dream material in various fields due to its stability and unique electrical and optical properties.

**Secret of Angles**

**Soccer Ball made by Scientists**

Kroto, Curl, and Smalley, who won the Nobel Prize in Chemistry in 1996, discovered Buckminsterfullerene, C60. They found that 60 carbon atoms are arranged like a soccer ball. Fullerenes have the shape of a truncated dodecahedron, consisting of 12 pentagons and 20 hexagons, and the pentagons are surrounded by hexagons. Fullerene is a dream material in various fields due to its stability and unique electrical and optical properties.

Secret of Angles (Chemistry)

The balloons shown here are modeled after a metal-organic polyhedron, which is a polyhedral chemical consisting of a metal (M) and an organic linker (L). Here we have a cuboctahedron (M12L24, small-sized balloon), rhombic cuboctahedron (M24L48, medium-sized balloon), and an unnamed polyhedra (M48L96, large-sized balloons). The actual metal-organic polyhedron is nanometer-sized that cannot be seen even with a microscope, and the same length of organic connector is used for synthesis. The shape or size of the organic linker varies depending on the angle difference when it is connected to the metal.

**Apices, Edges, and Faces of Polyhedra**

Secret of Angles (Chemistry)

The balloons shown here are modeled after a metal-organic polyhedron, which is a polyhedral chemical consisting of a metal (M) and an organic linker (L). Here we have a cuboctahedron (M12L24, small-sized balloon), rhombic cuboctahedron (M24L48, medium-sized balloon), and an unnamed polyhedra (M48L96, large-sized balloons). The actual metal-organic polyhedron is nanometer-sized that cannot be seen even with a microscope, and the same length of organic connector is used for synthesis. The shape or size of the organic linker varies depending on the angle difference when it is connected to the metal.

**Apices, Edges, and Faces** of Polyhedra

The discovery of symmetry was a great pleasure for scientists and mathematicians, and the problem of filling planes and spaces with symmetry was a way to express their own beauty.

**Beauty by Math**

**Apices, Edges, and Faces** of Polyhedra

The discovery of symmetry was a great pleasure for scientists and mathematicians, and the problem of filling planes and spaces with symmetry was a way to express their own beauty.

Beauty by Math (Math + Art)

If you look at the bathroom floor or sidewalk, the same shaped tiles are repeated, right? It is called tessellation, filling the plane with an identical shape.

The regular polygons that can be used in tessellation on their own are regular triangles, squares, and regular hexagons. The Penrose tiling is a tessellation using two or more polygons. Penrose tilings with two tiles, a kite, and a dart, have been proven by mathematician Roger Penrose to be arranged to create an aperiodic structure with regular patterns. This Penrose tiling became an important rationale behind the Nobel Prize in Chemistry 40 years later, the discovery of quasi-crystals.

**Math and Polyhedra in a Soccer Ball**

Beauty by Math (Math + Art)

If you look at the bathroom floor or sidewalk, the same shaped tiles are repeated, right? It is called tessellation, filling the plane with an identical shape.

The regular polygons that can be used in tessellation on their own are regular triangles, squares, and regular hexagons. The Penrose tiling is a tessellation using two or more polygons. Penrose tilings with two tiles, a kite, and a dart, have been proven by mathematician Roger Penrose to be arranged to create an aperiodic structure with regular patterns. This Penrose tiling became an important rationale behind the Nobel Prize in Chemistry 40 years later, the discovery of quasi-crystals.

**Math and Polyhedra** in a Soccer Ball

(Math + Sports)

Isn’t it surprising that polyhedra and math are hidden in the soccer ball we kick and play with?

The shape of a soccer ball is a truncated icosahedron, an Archimedean polyhedra, consisting of 12 regular pentagons and 20 regular hexagons. If you look at the history of the World Cup official ball, you can see that the shape has evolved to become closer to a sphere. Until the advent of the ‘Telstar’ in the 1970 World Cup in Mexico, mathematicians helped to find the ideal soccer ball shape (polyhedron) using Euler’s mathematical formula called polyhedron theorem.

**Math and Polyhedra** in a Soccer Ball

(Math + Sports)

Isn’t it surprising that polyhedra and math are hidden in the soccer ball we kick and play with?

The shape of a soccer ball is a truncated icosahedron, an Archimedean polyhedra, consisting of 12 regular pentagons and 20 regular hexagons. If you look at the history of the World Cup official ball, you can see that the shape has evolved to become closer to a sphere. Until the advent of the ‘Telstar’ in the 1970 World Cup in Mexico, mathematicians helped to find the ideal soccer ball shape (polyhedron) using Euler’s mathematical formula called polyhedron theorem.

How did you like our exhibition?

Please let us know your questions and suggestions.

**Address** 50 UNIST-gil, Bldg 108, 701-7 Ulsan 44919 Rep. of Korea

**Phone** +82 52 217 2546

Copyrightⓒ2018 UNIST. All rights reserved.

How did you like our exhibition?

Please let us know your questions and suggestions.

**Address**

50 UNIST-gil, Bldg 108, 704-7 Ulsan 44919 Rep. of Korea

**Phone
** +82 52 217 2546

Copyrightⓒ2018 UNIST. All rights reserved.