ManyFolds in Variety

It was found at the remains of folded structures this week:




Its shape, being restored into some symbolic design, seems as if it might be used in an ancient space opera series...

Material: a sheet of origami, without using adhesives.

Date: In May 2004

Photo date: March 26, 2005

This object is formed by helical folding similar to a study, "A convolution of paper in stripe", and is made of translucent paper.
Here is the whole image:



Almost the same structure made of thin tracing paper has appeared at the beginning of the article "Beauty of Convolution" Azuma Hideaki's spirals on the quarterly magazine ORU #6 (1994 Autumn).

Material: a sheet of translucent paper, without using adhesives.

Date: September 18, 1995 [as finished; not be done in one day]

Photo date: February 12, 2002

This study shows how the paper in rather wide width is folded in convolution, thanks to its stripes:


The folded object is also viewed as an almost/approximately helical piled up structure over a disc (more precisely, an annulus).

Material: a sheet of striped paper, without using adhesives.

Date: In August, 1995

Photo date: March 20, 2005

Somebody said to him, "it seems to be a pineapple."

This is also similar to Helical piled up structure over a hexadecagram, indeed, these two objects are composed in the same method of folding and formed into spatial shapes with some help of elasticity of material/paper; but there is a difference between two of these as mathematical conceptual folding: there is no regular polygon that coincides its 'plural' vertices with this helical folded structure.


If there exist a flat tape with infinite length, it will 'almost' cover an annulus in a plane by the helical folding in this case as mathematics: i.e., countable infinite number of all vertices set on that tape for helical folding should be placed dense in the circumscribing circle of the annulus, while countable infinite number of creases (in blue as the drawing above) formed by folding should be tangent to and surround the inscribing circle of the region in dense.

The helical folded and piled up object of yellow translucent paper and the single layer of the strip made of tracing paper under folding as a diagram in the above image, both were displayed side by side with the object and layer of a strip these shown in "Helical piled up structure over a hexadecagram" at the Second International Meeting of Origami Science and Scientific Origami, held at Seian University of Art and Design, Otsu, Japan, November 29-December 2, 1994.

Material: strips of translucent paper, with the use of adhesive tapes
[to stick together short strips side by side into a long one enough to fold and pile up].
(As far as the paper in use to fold this yellow object is concerned ;
If there exists a strip of appropriate length, then the description becomes as follows:
Material: a 'long enough' strip of paper, without using adhesives.)

Date: in 1993-4 [confirmation is in progress...]

Photo date: March 21, 2005

A long enough strip piled up into a helical coiled structure by the same method for folding the other object in convolution, with some help of physical property of paper:



An isosceles triangle which consists of two edges of equal length from hexadecagram{16/3} and the bottom edge from hexadecagram {16/6} (see the drawing at right side of the above image) is the basic unit to pile up a helical structure over the hexadecagon that circumscribes two hexadecagrams {16/6} and {16/3}.

In geometric conceptual folding, a strip is folded into a hexadecagon on the two dimensional plane, not coiled into a three dimensional body; but actually (and fortunately?), folding is done in the real space with real materials. Physical property of paper, particularly its elasticity, permits to pile it up into a helical coil and produces its slightly twisted shape: its larger picture is here.
The object made of pink translucent paper and the single layer of its strip under folding as a diagram in the above image, both were displayed at the Second International Meeting of Origami Science and Scientific Origami, held at Seian University of Art and Design, Otsu, Japan, November 29-December 2, 1994.

Another object in the same shape made of tracing paper has appeared in the article "Beauty of Convolution" Azuma Hideaki's spirals on the quarterly magazine ORU #6 (1994 Autumn).

Material: strips of translucent paper, with the use of adhesive tapes [to stick together short strips side by side into a long one enough to fold and pile up].
(As far as the paper in use to fold this pink object is concerned;
If there exists a strip of appropriate length, then the description becomes as follows:
Material: a 'long enough' strip of paper, without using adhesives.)

Date: in 1993-4 [the same but smaller one that was folded at December 4, 1993 is still preserved in his files of folding samples on convolution]

Photo date: March 21, 2005