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#1 2020-06-28 02:40:30

pi_cubed
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From: A rhombicosidodecahedron
Registered: 2020-06-22
Posts: 77

Flexagons

Flexagons are flat models that are usually constructed by folding strips of paper into geometric shapes. They can be "flexed", or folded in certain ways, to reveal hidden faces. They were discovered by Arthur H. Stone and popularized by Martin Gardner.

Equation for finding number of individual polygons on a strip for a flexagon that has a certain amount of faces and a number of polygons in each face:

``f*n``

Where f is the number of faces and n is the number of polygons on each face.

More flexagons: http://loki3.com/flex/
Flex theory: https://www.gathering4gardner.org/g4g10 … Theory.pdf

pi³

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#2 2020-06-29 09:20:48

Mathegocart
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Registered: 2012-04-29
Posts: 2,146

Re: Flexagons

Hmmmm, interesting. Recreational mathematics has always been a side hobby of mine.

The integral of hope is reality.
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#3 2020-07-15 02:22:00

666 bro
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From: Flatland
Registered: 2019-04-26
Posts: 658

Re: Flexagons

Mathegocart wrote:

Hmmmm, interesting. Recreational mathematics has always been a side hobby of mine.

Recreational maths is always fun.

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#4 2020-07-15 02:53:54

ganesh
Registered: 2005-06-28
Posts: 34,878

Re: Flexagons

Everyday, every moment is a learning experience.

Today, I learnt a new concept.

flexagon : (noun)

a folded paper figure that can be flexed along its folds to expose various arrangements of its faces
or
a flat model consisting of a single pliable strip of paper which can be folded and flexed in various ways to expose different hidden faces
or
a three-dimensional figure having polygonal faces that is constructed from a folded sheet of paper in such a way that different faces are exposed when the figure is flexed along its folds.

In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.

Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix can be added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a hexaflexagon with a total of six faces is called a hexahexaflexagon.

In hexaflexagon theory (that is, concerning flexagons with six sides), flexagons are usually defined in terms of pats.

Two flexagons are equivalent if one can be transformed to the other by a series of pinches and rotations. Flexagon equivalence is an equivalence relation.

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