No. 70
Philip Shen: More Paperfolds MoreGeometric Geometric Folds
Boaz Shuval
No. 70
©Models by Philip Shen ©Diagramss - Boaz Shuval ©Diagram Compilation published by British Origami Society, January 2008
More Geometric Paperfolds is BOS Booklet No. 70
Printed in the United Kingdom. All rights r ights reserved. No part of this publication may bereproduced,storedinanyretrievalsystem,or transmitted,inanyformor byany means, electronic, mechanical photocopying, photocopying, recording or otherwise without the express written permission of the author and of the British Origami Society. The British Origami Society Society is a registered registered charity. Charity Number 293039 www.britishorigami.info
More Geometric Paperfolds Philip Shen Compiled by Boaz Shuval
Preface and acknowledgements Philip Shen has always been on my list of top origami artists. My first exposure to his work was in Paul Jackson’s excellent book (now sadly out of print), “Classic Origami”. The model diagrammed there, Shen’s Incense Burner, was unlike anything I had ever folded before. It seemed like I was folding aimlessly, creating a beautiful pattern of creases. Then, in a magical move, the creases are brought together and the clean, complete, and beautiful form of the model emerges. I started seeking for other models by Shen. They were hard to find, and most were collected Paperfolds”.. I enjoyed each and every in Paul Jackson’s BOS booklet No. 18 “Selected Geometric Paperfolds” one of these, but I was still on the lookout for more. A few more models by Shen, I found, thanks to the Origami Database, were diagrammed in out of print publications, such as old BOS magazines, old BOS convention books etc. Alas, these models are not easily obtainable. In August 2004, I relocated from Israel to San Diego, California. Shortly before my move, I learnt that Philip Shen lived close to San Diego, about 2 hours away. One of the first things I did after I landed was to contact Mr. Shen. To my dismay, I discovered that he had passed away only days earlier. It was then that I decided to collect as many of Shen’s Shen’s works as I could and to publish them as a tribute. This collection is the first fruit of these efforts. To diagram these models, I had to very carefully unfold models by Shen, and find a method of folding. Most Shen models employ a similar folding process: first, the folder makes a series of folds that produce a beautiful geometric, symmetrical, crease pattern on the paper. Then, the folder manipulates these folds in a way that locks them in the final form. So, to diagram the models I had to find a way to reproduce the crease pattern as easily as I could without adding extra creases, and then to find a method of collapsing everything into place. Luckily, many of the models utilize similar geometries (such as 30 and 60 folding), but some cases were hard nuts to crack. ˚
˚
Discovering these models, finding folding methods for them, and diagramming them has been a joy for me. I hope that the models collected here bring you as much joy as they have brought me. Of course, if you know of any Shen models that are unpublished, please contact me, as I am intereste interested d in finding out about them. My e-mail address is:
[email protected] This collection would not have been possible without the help of several friends: first and foremost, I would like to thank Paul Jackson, who generously provided me access to his his private collection of models by Shen (most models diagrammed here are from his collection). Second I would like to thank Yee-Nar Yuen, a student of Shen’s whom I met at an origami convention. Yee-Nar has been an enormous help in providing me with information about Shen and also some more models from her collection. Shen’s waterbomb lock has been extremely difficult for me to obtain. I had heard about it but could not find how to make it anywhere. Finally Joanne Ortman provide provided d me with the information on this fold, and I thank her for this. I would also like to thank Mrs. Sylvia Shen, who has given me permission to publish this collection, and the British Origami Society for allowing me to publish this collection as part of their series of booklets. Finally, I would like to thank Nick Robinson for proof-reading the diagrams and providing valuable input.
Table of Contents 10 Pointed Star 30 Degree Dish Cot Crown Bowl Flower Basket Flower Dish Hexagonal Container Icosahedral Bowl Modification of the Chinese Vase Pentagonal Flower Petal Dish Rose Dish Shen’s Waterbomb Lock Snowflower Star Box Triangular T riangular Dish
9 12 13 15 20 22 24 26 29 32 34 36 40 42 44 45
BOS Publications
48
7
Folding Tips Most of Shen’s models were created without a preconceived model in mind. Rather than trying to design a model with specific traits, Shen enjoyed taking a piece of paper and folding it until a model emerged. This is a process of exploration and discovery. The models in this booklet should be folded with that in mind. In fact, as you fold these models, you will become familiar with some of the geometries that Shen employed. Do not be surprised if you find yourself adding creases in an attractive pattern to a piece of paper and trying to flex them to lock in a certain position. There are several threads running through all these models. First, the models are clean: they use the minimum number of creases and points, preferably without any unused creases. Secondly, the final model is attractive, usually geometric and somewhat abstract, and it is usually 3-dimensional and contains curved surfaces. Keeping in line with the ideas above, crease sharply and cleanly throughout the pre-creasing stage, unless instructed otherwise. Do not crease beyond what is indicated, because you do not want any unwanted creases. Most importantly, though, you should enjoy the folding. What paper should you use for folding these models? Shen himself used to collect various scrap papers and use them. Many of his models were folded from thin, clear, vellum. In this medium every crease is clearly visible, and with Shen’s models it provides a pretty effect. Another type of paper frequently used by Shen is souppacket wrapping (of Knorr brand). The wrapping has a shiny, silvery side, which should be used as the “coloured” side of the paper. This material is generally not very useful for folding, but with Shen’s models it works well. Not all the models in this collection are folded from squares. Some are from triangles, some are from hexagons, and some are from pentagons. I have deliberately not provided instructions for making these forms. There are many methods, and you should choose the method you are most comfortable with. I suggest you make yourself some templates and use these in order to obtain starting forms that are free from creases, or that have creases only along heavily utilized lines of symmetry (such as diagonal and altitudes).
8
10Pointed pointedStar 10 s ta r
If you were to receive this model by mail from Philip Shen, this is what you would have found in the envelope: a 10 pointed star that when unfolded reveals an intricate net of creases of various colors and instructions on how to form them to create the model yourself. In the instructions for this model, we will use the same approach. The drawings that follow correspond to the steps as appearing on the crease pattern. Collapsing instructions will appear as a sequence of images.
If you were to receive this model by mail from Philip Shen, this is what you would have found in the envelope: a 10 pointed star that when unfolded reveals an inticate net of creases of various colours and instructions on how to form them to create the model yourself. 7 In the instructions for this model, we will use the same approach. The drawings that follow correspond to the steps as appearing on the crease pattern. Collapsing instructions will appear as a sequence of images.
9
1b 1a
Crease this larger star... (Do this by bringing the center of each edge to the height opposite. The points you should bring together are designated as black dots in the figure.)
... and the medium pentagon. (This pentagon is created by adding creases between the intersections intersections of the creases from step 1a.)
3
2
B 1/ 2
1/ 2
parallel parallel A Crease this smaller star. (The marked crease is created by bringing A to B.)
4
Crease this larger pentagon. (Do not crease on the dotted lines.)
10
Crease this small pentagon. (It is created by bringing the center of each edge of the medium pentagon to the center of the paper.)
5
Crease these crossing lines.
12
11
Completed 10 pointed star.
8
Repeat on all points.
10 9
Tuck the point under the inner pentagon. Fold the edges of the point to the center crease, incorporating a swivel (the thick lines are mountain folds). The pentagon is now flat on the table. Now, squash one point.
6
The following images show the collapse. Begin by pinching the corners and lifting the small pentagon. (Thick lines are mountains, dashed lines are valleys.)
7
Like so. Notice that the rhomboids near the inner pentagon penta gon remai remain n open. open. Twist the inner penta pentagon gon while while pushing it down. 9
11
30 Degree Dish i s h 30 Dish 3 0 D e g re e D ˚
1 2 3
6 5 4
7
Unfold one flap. Fold edge to crease shown. Crease only on one half of the square. Repeat 8 times. Bring point to point, but fold only where shown. Repeat 8 times.
Reverse the direction of creases as needed and bring towards the diagonal.
8 9
Continue folding towards diagonal, and lock by folding flap over.
12
Repeat three more times, on the three other edges.
Completed 30 degree dish.
Cot Cot
1 2
3
Use a duo-colored square. Crease only one diagonal.
Pinch the center of the edges shown.
4 5
6
7
8
Fold through all layers.
Fold the corners behind, and change the orientation of the creases shown to mountain.
13
15
Completed Cot.
Push down with your fingers to make the cot round. Make light creases on the surface of the bed following the x-ray creases.
14
13 12 Like so. Turn over.
Lock the corners by folding the corner Fold the sides back, and incorporate triangles in half. reverse folds on the corners. Do not make any creases on the top triangle.
10 9
Make the creases shown, but do not fold on the top or bottom of the paper. Make the creases shown, but do not crease in the center.
14
11
Crown Bowl Cn blw r o w o
1 2
3
5
4
6
Bring point to line through corner, but fold only where shown. Repeat on other corner and on back.
7
8
9
4 – 6
Unfold back to step 4. Repeat steps 4-6 on the other two corners.
15
18 17 16
Fold using reference pinch as guide.
15
14 13
Pinch to mark reference point. Unfold back to step 12. Pleat the corner lightly.
12
11 10
Extend the crease, but crease lightly. Do not repeat.
Extend the crease, but only in the center square. Repeat 8 times.
16
19 20
21
Unfold back to step 16.
22
21– 23
24
25
23
Unfold back to step 21. 21– 23
Repeat steps 21-23 on other two corners. Unfold completely.
26
27 28
Unfold back to step 25. 1
17
36 35 34
Like so. View from inside reverse folded corner. Bring sides together.
Like so. View from the top. Reverse fold one corner along existing creases.
33
Put in folds based on creases from steps 26-27. Repeat steps 34-36 on all corners.
32
In progress. This view is from the inside (underneath) of the “V”.Repeat on all sides. Like so. Close the “V” shape from step 30, and bring sides down using precreases.
31
30
25– 28
29
Collapse. Center point should go inwards. Circled points should be convex (pointing upwards)
25– 28
18
Change orientation of creases as shown.
37 38
Done. Insert thumb into rounded caps, and smooth out top of inverted “V”s. Insert finger into “V” cups, and round bottom. See close-ups for finished move. Open small diamonds, and smooth them from the inside.
39 40
Front diamond open. Continue opening diamonds, and turn over.
41 Push convex point inward to lock model.
Locked. Turn over.
Completed crown bowl.
19
Flower Basket FB lo ak w e r s te k
1 2 3
Mountain-fold in half.
6
5
4
7 5 – 6
Tuck behind.
Squash.
8 9
Fold two diagonal creases through the center. It is easy to do if you line-up creases as shown.
20
10
This fold is similar to a preliminary fold.
20
19
Completed flower basket.
Open basket. Round the handle. Close sides again
18 17 16 Fold over twice.
15 Mountain-fold both layers. 11 – 14
Open front flaps only.
Repeat steps 11-14 behind.
14 13 11
12
12 – 13
21
Flower Dish Flowe r d is h
1 2
3 4 4
5 6
Bring point to point, but fold only where shown. Repeat 8 times.
7 8 5 – 7
9
5 – 7
5 – 7
22
Unfold.
16
Completed flower dish.
Tucked. Flap is shown darkened for clarity only. Repeat steps 12-14 on the other three corners. When done, push bottom up from below.
15
Like so. Tuck dark flap inside pocket to lock.
14 13
In progress. You may have to change the direction of some creases as you collapse.
Collapse as shown.
12
10
11
Precreasing completed
Fold only where shown.
Fold between the points. Repeat steps 9-10 on the the other three sides.
23
Hx etn Hexagonal Container a Hexagonal Container g o ln C o iea r
1 2
3 Begin with a hexagon.
4
5
Repeat 6 times.
Only fold between the dots. Repeat 6 times.
6 7
24
14
Completed Hexagonal Container. Push in sides to make container 3D.
13
11–12
11–12
11–12 11–12 11–12
11 12
10
6 – 9
6 – 9
6 – 9
8
6 – 9
6 – 9
9
23
25
Icosahedral Bowl
Icosahedral Bowl I ce oo s a h d a lr B w 1 2 3
Begin with an equilateral triangle. Mark the center of each edge. Fold each corner to the center crease. Fold each edge to opposite crease from step 2.
4
6
5
7 4–5
4–5
Rabbit-ear.
Repeat steps 4-5 on other two corners
Add precreases. Fold rabbit-ear down.
8
Make a pleat, keeping the circled dot convex (pointing at you). Tuck pleat inside rabbit-ear pocket. pocke t. The The model model becom becomes es 3D. 3D.
26
9
Repeat on other two corners.
Completed bowl. This is half of an icosahedron.
Icosahedral - Variation 1 1 Icosahedr Icos ahedral alBowl Bowl - Variat Variation ion I c o s a h e d r la B o l-w V1 a tir o n
1 2
Begin with step 4 of the icosahedral bowl. Add the creases shown. shown. Now continu continuee folding folding the the icosahedra icosahedrall bowl from step step 4.
3
Fold along creases from step 1. You will have to straighten some creases to complete this step.
Completed.
27
Icosahedral Bowl - Variation Variation 2 Icosahedral Bowl - Variation 2 Ica oa s hB e d r l -lw o Vaa r i tn io 2
The folding of this model is very similar to that of variation 1. The difference between the two models is that here there is a hexagon in the center of the triangle, rather than a triangle. By now you should have enough experience with this model to be able to construct the creases shown without further instructions. The outcome is a dish with a curved hexagonal bottom.
28
Mf d ifoe f a ic n fo th Modification of the Chinese C h i n Vase s e V a s e
1 2
3
Fold and unfold in half in both directions. Do not crease at the cen ter.
Crease thirds.
5
4
Crease the center square by folding each edge to the center marks and creasing in the center.
1/4 1/3
1/2
6
1/3
7
8
Precrease, then unfold steps 5 and 6.
29
15 14
Precrease by folding back and unfolding each corner of the petal folds. (Arrows are shown only on one corner to reduce clutter.
Incorporate a petal-fold in each of the center pleats.
13
12 11
Collapse completed. Turn over. In progress. Persevere.
Collapse using existing creases. Mountain folds are shown using thick black lines, and valley folds using gray dashed lines.
10 5 – 9
9 1/4 1/3
5 – 9 1/2
Crease where shown, and change crease genders as indicated.
30
5–9
16 17
Tuck the right and left flaps under the pleat.
18 19
20 Puff up the octagon at the bottom botto m of the vase vase.. See See next next step for details.
Tuck the corners under using the precreases from step 15. Note that there are two pockets you can tuck the corners into; tuck it into the top pocket.
Puff up the octagon at the bottom of the vase vase using existing creases.
21
Like so. Pinch the corners slightly (insert fingers into pockets from other side if necessary) to shape the vase.
Completed modification of the Chinese Vase.
31
Pentagonal Flower Pentagonal Flower Pe e t g o n F la rw
1 2
Use a pentagon, colored differently on each side. Add folds as shown. Bring each edge to the center to fold the inner pentagon.
3 4 5 Fold each edge of the inner pentagon to the center and unfold.
Fold the inner pentagon. Note reference points. Crease lightly.
6 7
32
8
15
Completed pentagonal flower.
14
Reform the squashes to lock flower.
13
Collapse. The light creases are valleys and the dark ones are mountains.
10–12
10–12
10–12
Repeat steps 10-12 three more times. You will have to unfold some of the squashes. Unfold completely.
12
11 9
10 Squash along hidden crease.
33
Petal Dish P e a t lD is h
1 2
3
Use a duo-colored square. Divide into thirds, but do not crease the center.
4 6
5
7 5–6 4–7
8
34
9
15
Completed petal dish. Like so. If you like, you may pre-crease the mountain folds before making the model three dimensional, but I find it easier to approximate them at this stage. Repeat on all three corners.
14 13
Indent petal with your finger. Make two mountain creases on the inner side of the petal. The mountain creases should be approximately at a 90 degree angle to the edge. Make a curved crease on the outer side of the petal. See next step for details.
12
11 10
3D view. With the flap lifted, strengthen the existing mountain folds.
Insert your finger into the pocket, and lift the flap.
33
35
Rose Dish h is d e R o
1 2
3
4 5
Unfold one of the flaps of the blintz. Bring point to point, but fold only where shown.
6
7
4 – 6
4 – 6
4 – 6
Repeat steps 4-6 three more times and unfold.
36
13 9 – 12
12
9 – 12
9 – 12
Repeat steps 9-12 on other three flaps. Page turn.
11
10
As you bring point to point, the mountain fold will form naturally. Unfold back to step 9.
Bringing the corner of the front flap to the intersection between the crease of step 9 and the diagonal. Crease halfway halfway..
9
8
Bring the corner of the front flap to the point shown and crease. Fold into a preliminary fold using existing creases.
37
15
14
Fold and unfold on the top layer only.
Fold and unfold on the top layer only.
14–15
16 14–15
14–15
17 Repeat steps 14-15 on the other faces.
18 Start to fold
19
In progress. Wrap lower layer behind.
17–18
20 17–18 17–18
Like so. Repeat steps 17-18 on the other flaps.
38
Fold and unfold. Repeat on the other flaps.
26
Completed Rose dish. Push the bottom inwards, lift the flaps, and push the petals inwards slightly.. Curl the petals. slightly
25
24 Open and fold behind the rest of the flaps in the same manner.
Keep opening and fold behind.
22 21
23
Insert your finger into flap and open it.
Open into a cup. Curl each of the flaps lightly lightly.. 37
39
Shen’s Waterbomb Lock Shen’s k c o L k mb o b r te s a ’W n e Sh
1 2
3 4
5 6
Fold a waterbomb base.
Pinch.
Fold both flaps to center crease. Repeat behind.
Bring front corners to crease mark.
7 8 9 10 Fold back flaps behind, along the folded edge. Fold flap over folded triangle. Like so. Unfold.
40
Up to here, this is just like the regular waterbomb. The following sequence of steps is Shen’s improved lock.
18
17 Blow into the hole and shape into a waterbomb.
Completed waterbomb.
16 15
8 – 15
14
8––15 15 8
Repeat steps 8-15 on the rest of the flaps. Like so. Fold flap back down.
13
11
Fold the little triangle behind the flap, using existing crease. Bring flap back to unlifted position.
12
Fold over triangle (over existing crease) Lift flap. Insert finger under flap, and “yank it open”.
41
n fS f lo w e r Snowflower
1 2
3 Begin with a hexagon.
4 Repeat 6 times.
5 Bring the hollow dots together together.. Only fold between the black dots. Repeat 6 times.
6
Fold angle bisectors in each little triangle of the innermost hexagon. Do not fold beyond the diagonal.
42
11
Completed snowflower s nowflower.. The model is called snowflower because it resembles a snowflake. In Chinese, the word for snowflake is written using two characters, the character for “snow” and the character for “flower”. Insert your fingers into each of the petals, and open them.
10 9
Pinch each ridge, and collapse center along existing creases. Push center upwards from below (center should point up).
Fold edges of outer hexagon in, along existing creases. Do not add any new creases. 2
1
8 7
Like so.
Collapse according to indicated creases. Arrows are shown for one portion only. only.
43
Star Box Sb ta rx o
1 2
3
5
4
6
7 11
Completed Star box. Fold one corner at a time, working in a clockwise order to make the star box.
44
Triangular Dish h s i D r a l u g n Tria 1 2 3
Begin with an equilateral triangle. Mark the center of each edge lightly. Fold each corner to the center crease. Fold each edge to opposite crease from step 2.
4
6
5
Only fold where shown.
7
8
9
Petal fold.
4
45
16 15
Fold on existing creases from step 6.
Fold along existing creases. Marked dots will become concave.
14
13
Precreasing is finally done. Turn over.
Bring point to point, but crease only where shown. Repeat 5 more times.
10
11 Bring point to point, but crease only where shown. Repeat 5 more times.
5 –10
Like so. Unfold back to step 5.
46
12
5 –10
Repeat steps 5-10 on other two corners. For clarity, not all creases will be shown in the following steps.
17
18
Insert your finger inside the pocket, and bring corner down using existing creases (light crease is a mountain). Curve edges of bowl as you do this. Next step step will show the view from from the pocket.
View of step 17, from the pocket.
19 20
Like so. The next step will view the model from above.
Petal fold flap on existing creases from step 10.
21
Like so. The edges of the dish curve naturally. Repeat steps 17-20 on the other corners.
Completed triangular bowl.
47
BOS Publications 1
History of Origami
John Smith
2
Origami and Mathematics
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History of Origami in Britain
David Lister
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Origami Instruction Language
John S Smith
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Teaching T eaching Origami Origami
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Geometric Division
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Chess Se Setts of Ma Mart rtiin Wall, Ma Max Hume & Neal Elias
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Napkin Folds
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Origami and Magic
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Neal Elias: Selected Works 1964-1973
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Flexagons
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Martin Wall: Early Works 1970-1979
Martin Wall
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Orikata
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Pureland Origami 1
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Max Hume: Selected Works 1973- 1982
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18 of My Paper folds
Paul Jackson
17
Origami Games
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18
Philip Shen: Selected Geometric Paperfolds
Paul Jackson
19
Tony T ony O’Hare: O’Hare: Selected Work Workss 1973:1982
Daniel Mason
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Origami Christmas Tree Decorations
Paul Jackson
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The Silver Silver Rectangle
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In Praise of the Bird Base
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Index: BOS Magazine 1-100
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Index: BOS Magazine 101-120
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Envelope and Letter Folds
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Animal Origami
Edwin Corrie
27
Origami
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28
Structural Reconstruction
Ricky Wong
29
Pureland Origami 2
John S Smith
30
Paper People and Other Pointers
David Petty
31
Mor ’igami
Jeff Benyon
32
Patterns in Paper
John S Smith
33
Animal Origami 2
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Neal Elias: Miscellaneous Folds I
Dave Venables
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Neal Elias: Miscellaneous Folds II
Dave Venables
36
Neal Elias: Faces and Busts
Dave Venables
37
Jeffori 3
Jeff Benyon
38
Four ‘igami
Jeff Benyon
39
Animal Origami 3
Edwin Corrie
40
Genius of Jan Willem Derksen
David Petty
41
Index: BOS Convention Packs
David Petty
42
Larry Hart: Selected Works (1971-1991)
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Pureland 3: Smith
John S Smith
44
Multi’plication
Jeff Benyon
45
The Origami Origami of Stephen Palmer
David Petty Petty
46
Modular Construction and Twists
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47
ABC of Origami
Eric Kenneway
48
Making Faces
David Petty
49
World of Fred Rohm I
Pete Ford
50
World of Fred Rohm II
Pete Ford
51
World of Fred Rohm III
Pete Ford
52
Origami Models Folded from Rectangles
John Morgam
53
Origami Models Folded from Silver Rectangles
John Morgan
54
More Origami Models Folded from Silver Rectangles
John Morgan
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Sink or Swim with Ted Normington
Ted Normington
56
Petal Folds and More
Ted Normington
57
Pureland 4
John S Smith
58
Owrigami
Francis Ow
59
10 Pop-Ups
John S Smith
60
A Medieval Court in Origami
Julia Pálffy
61
Decorative Boxes from Single Squares
Arnold Tubis & Leon Brown
62
Animals and Birds
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63
Ship-shape and Bristol Fashion
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64
Faces’n’Fings
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65
Planar Modulars (CDRom)
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The Nativity Nativity - An Origami Scene Scene
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Quentin Trollip - Selected Works
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Which Came First
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3D Masks and Busts
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Phillip Shen: More Geometric Paper folds
Boaz Shuval
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My Fundamentals
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Occasional Booklets
Paperplay
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Bibliography: Origami in Bibliography: Education and Therapy
John S Smith
COET
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Other Booklets
Fold with Feeling
Nick Robinson
Hearts 3D
David Petty
Origami Favourites
Edwin Corrie
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10 pointed star 10 point Star page 79 Page
Flower Basket Flower basket page Page1820
Modification of the Modification of Chinese vase Chinese Vase page 27
Page 29
Shen’s Waterbomb Lock Waterbomb Lock page 40 38 Page
30 degreeDish dish 30 Degree page12 10 Page
Flower FlowerDish dish page22 20 Page
Cot Cot page Page 1311
CrownBowl bowl Crown page 15 13 Page
Hexagonal Container Bowl Hexagonal Container Icosahedral Icosahedral bowl page page 26 24 Page 2422 Page
Pentagonal Flower Pentagonal flower Page 32
Petal Dish
page 30
Petal dish Page 34 page 32
Snowflower Snowflower page 42 40 Page
Star Box Box Star page 44 42 Page
Rose Dish Rose dish Page 36 page 34
Triangular dish Triangular Dish page Page43 45 47
