The Public Paperfolding History Project

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Constructing Polygons by Folding Paper
 
This page attempts to record what is known about the origin and history of how to construct polygons by folding paper. Please contact me if you know any of this information is incorrect or if you have any other information that should be added. Thank you.

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The Equilateral Triangle

1863

An illustration which depicts the construction of an equilateral triangle from a square appears in 'De Kleine Papierwerkers 1: Wat men van een stukje papier al maken kan: Het vouwen' (The Small Paperwork 1: What one can make from a piece of paper: Folding) by Elise Van Calcar, which was published by K H Schadd in Amsterdam in 1863.

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1873

'Die Praxis Des Kindergartens' by Auguste Koehler, which was published by Herman Bohlau in Weimar in 1873, contains a folding sequence which produces an equilateral triangle.

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1940

A method of constructing an equilateral triangle from a square is found in 'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940.

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The Diamond / 60/120 degree Rhombus

1836

An illustration which depicts the construction of a diamond from a bronze rectangle appears in 'De Kleine Papierwerkers 1: Wat men van een stukje papier al maken kan: Het vouwen' (The Small Paperwork 1: What one can make from a piece of paper: Folding) by Elise Van Calcar, which was published by K H Schadd in Amsterdam in 1863.

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1873

'Die Praxis Des Kindergartens' by Auguste Koehler, which was published by Herman Bohlau in Weimar in 1873 contains a method of producing a diamond from a square.

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1940

A method of constructing a 60/120 degree rhombus from an equilateral triangle is found in 'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940.

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The Regular Pentagon

A method of constructing a regular pentagon from a square is found in 'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940.

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The Regular Hexagon - 1682 onwards.

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Hexagrams / Stars of David

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The Regular Heptagon

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The Regular Octagon

1872

The second 'expanded and improved' edition of 'Das Frobel'sche Faltblatt' (Frobel's Folding Sheet) ) by August Kohler, which was published by Hermann Bohlau in Weimar in 1872, contains a method of constructing a regular octagon by folding each corner inwards in turn to lie on the diagonals. I cannot find any reference to this technique in the text of the book.

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1877

A method of constructing a regular octagon from a singly blintzed square is given in 'Cours de Travail Manuel (Pour les Garcons) - Premiere Partie - Cours Elementaire' by A Planty, which was published by Gedalge Jeune in Paris in 1887. Tthere are no location points for the folds that blunt the corners of the square.

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1891

There are references to constructing octagons by paperfolding in the 'Bulletin de la Societe de Protection des Apprentis', an official document issued by the Societe de Protection des Apprentis et des Enfants Employes par les Manufactures in Paris in 1891 but no instructions are given..

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1892

Two methods of constructing an octagon by folding a square are found in 'Le Travail Manuel a L'ecole Primaire' by Jully & Rocheron, which was published by Librairie Classique Eugene Belin in Paris in 1892.

Filtre / Octagone

The octagon is made by joining the ends of the relevant creases.

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Autre pliage de l'octogone / Folding an octagon - another method

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1895

'L'enseignement manuel dans les ecoles du degre primaire (garcons)' by Rene Leblanc, which was published by Librairie Larousse in Paris in 1895, also explains the first method shown above.

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1940

Two further methods of constructing a regular octagon are found in 'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940.

Construction of a Regular Octagon from Two Squares

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Construction of a Regular Octagon from a Single Square

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The Regular Decagon

1940

A method of constructing a regular decagon from a regular pentagon is found in 'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940.

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The Regular Dodecagon

1891

There is references to constructing a dodecagon from a hexagon in the 'Bulletin de la Societe de Protection des Apprentis', an official document issued by the Societe de Protection des Apprentis et des Enfants Employes par les Manufactures in Paris in 1891. Details of the method are not given.

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1909

A method of constructing a dodecagon from a hexagon appears in 'Petit Manuel de Travaux d'Amateurs' by H de Graffigny, which was published by Collection A L Guyot in Paris in 1909.

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1940

Another method of constructing a regular dodecagon from a regular hexagon is found in 'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940.

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Oblongs

'At Home Tonight' by Herbert McKay, which was published by Oxford University Press in London, New York and Toronto in 1940, gives a way of constructing an oblong from an irregularly shaped sheet of paper.

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Parallelograms

A method of constructing a 45 / 135 degree parallelogram from a square is found in 'El Plegado y Cartonaje en la Escuela Primaria' by Antonio M Luchia and Corina Luciani de Luchia, which was published by Editorial Kapelusz in Buenos Aires in 1940.

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