twirls -origami models based on the polyhedra …...twirls -origami models based on the polyhedra...

Twirls - origami models

based on the polyhedra structures

Wojciech Burczyk, PhDwww.origami.edu.pl

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www.origami.edu.pl

burczyk@mail.zetosa.com.pl

Conference of AMTL Creativity in the Mathematics’ Education

September 24th-25th, 2010, Līvāni, Latvia.

Base modules

SLSL SSLL

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SSFF sunk SSFF

SFSF SSSSsunkSFSF

Macro-modules correspond to polygons

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Assembly of macro-modules, single outer

spiral

Macro-modules with single outward spirals (SLSL, SFSF) are assembled in two different ways.

– edge to edge;– vertex to vertex.

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Assembly of macro-modules, double outer

spirals

It is possible to assemble macro-modules with double outward spirals (SSLL, SSFF)in four different ways.

– edge to edge;– vertex to edge;– vertex to vertex;– a double spiral vortex to a double spiral vortex.

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– a double spiral vortex to a double spiral vortex.

Edge to edge assembly (single outward

spiral)

SLSL

+ +

6

+ =

Vertex to vertex assembly (single outward

spiral)

SLSL

+ +

7

+ =

Edge to edge assembly (double outward

spiral)

SSLL

+ +

8

+ =

Vertex to edge assembly (double outward

spiral)

SSLL

+ +

9

+ =

Vertex to vertex assembly (double outward

spiral)

SSLL

+ +

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+ =

Vortex to vortex assembly (double outward

spiral)

+ +

SSFF

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+ =

Test your knowledge about symmetry and try

to find a polyhedral structure in twirl models

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to find a polyhedral structure in twirl models

Can you see a polyhedron?

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Different structures – the same model

Can you see a polyhedron?

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Duality

Can you see

a polyhedron?

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Duality

Can you see a

polyhedron?

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Similar appearance, but different structure

Can you see

a polyhedron?

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Different appearance, but the same structure

More about twirl kusudama

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Thank You!

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