# Handlebody and Knot composed of polygons

• A
• GEOPHILE2
In summary, the conversation is about finding literature on constructing topological structures using geometric composition, specifically involving polyhedra, polygons, lines and points. The conversation mentions Professor George Hart as a potential source and also includes a link to his website. The person posting is interested in articles or books on constructing knots, links, tori/handlebodies, and Mobius strips with geometric composition, and signs off with "Happy Holidays" and the name "GEOPHILE2".
GEOPHILE2
Has anyone seen any literature related to the construction of topological structures with geometric composition as seen below?

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Do you mean specifically? Or are you generally interested in physical constructions of mathematical objects? George Hart (father of Vi Hart, famed quirky creator of math videos) does some amazing constructions. http://georgehart.com/

Hi, thank you for the reply and the link to Professor Hart's web page. As to the photo I posted, I was hoping for any articles or books that are about constructing topological structures such as knots, links, tori/handlebodies and Mobius strips with geometric composition as for instance polyhedra, polygons, lines and points specifically. Happy Holidays, GEOPHILE2

## 1. What is a handlebody?

A handlebody is a three-dimensional object with a genus, or number of holes, that can be formed by attaching handles to a solid ball. These handles can be thought of as tubes or cylinders that connect different parts of the ball together.

## 2. How are handlebodies related to knots?

A handlebody can be seen as a way to construct knots by taking a polygon and attaching handles to it. These handles can then be twisted and knotted to form a more complex structure, like a knot. Therefore, handlebodies and knots are closely related and can be studied together.

## 3. What is the difference between a handlebody and a knot?

The main difference between a handlebody and a knot is their dimensionality. A handlebody is a three-dimensional object, while a knot is a one-dimensional object. Additionally, handlebodies have a genus, or number of holes, while knots do not.

## 4. How can handlebodies and knots be represented mathematically?

Both handlebodies and knots can be represented using mathematical equations and diagrams. For handlebodies, a common way to represent them is through Heegaard diagrams, which involve attaching handles to a two-dimensional polygon. For knots, they can be represented using knot diagrams, which involve drawing the knot on a two-dimensional plane and indicating how the string crosses over and under itself.

## 5. What are some real-world applications of handlebodies and knots composed of polygons?

Handlebodies and knots have many applications in various fields, such as physics, chemistry, and biology. They can be used to model DNA and protein structures, study fluid dynamics, and understand the topology of physical systems. They are also used in knot theory, which has applications in areas such as cryptography and robotics.

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