Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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Mathematical Designs
 
Miscellaneous Mathematical Paperfolds
 
  Name: Point of Balance - a simple mathematical / engineering problem set and solved by folding paper.

Paper type / shape: Square / Irogami.

Designer / Date: David Mitchell, 1999.

Diagrams: On-line diagrams are available from the Mathematical section of this site.

 
  Name: Silver Fir - a semi-naive design.

Paper type / shape: Multiple squares of regularly diminishing size all cut from a single silver rectangle.

Designer / Date: David Mitchell, 2019

Diagrams: On-line diagrams are available on the Multiple Sheet Designs page of this site.

 
Tiles and polygons
 
Origami tiles are flat shapes derived by folding paper that will go together to form a tiling pattern. Origami polygons are flat shapes derived by folding paper. Some origami polygons will, of course, act as tiles as well.
 
  Name: Cairo Tiles

Paper type / shape: Various methods from squares, silver rectangles and leftover rectangles / Either homogeneous paper or irogami..

Designer / Date: David Mitchell, 2000

Diagrams: From leftover rectangles - (1) Exploring Mathematical Ideas with Origami - Water Trade - ISBN 0953477444 // (2) BOM295 December 2015 p18 // From squares and silver rectangles - Infinity 2005/2 - Tarquin publications ISSN 1748-3220 // Sticky note version from squares in Sticky Note Origami - David Mitchell - Collins and Brown - ISBN 1-84340-227-0 // Unattributed in Learning Mathematics with Origami - Tung Ken Lam and Sue Pope - 2016 - Association of Teachers of Mathematics - ISBN 9781898611950 // On-line diagrams for designs from squares, silver rectangles and leftover rectangles are available from the Mathematical section of this site.

 
  Name: Golden Proportion Tiles - twin triangular tiles with edges in the golden proportion.

Paper type / shape: Squares / Any kind of paper.

Designer / Date: David Mitchell, 2000.

Diagrams: Exploring Mathematical Ideas with Origami - Water Trade - ISBN 0953477444 // On-line diagrams are available from the Mathematical section of this site.

 
  Name: Penrose Tiles (kites and darts)

Paper type / shape: 2x1 rectangles / Any kind of paper..

Designer / Date: David Mitchell, 2000.

Diagrams: Exploring Mathematical Ideas with Origami - Water Trade - ISBN 0953477444 // On-line diagrams are available from the Mathematical section of this site.

 
  Name: Sphinx Tiles

Paper type / shape: Leftover rectangles or similar / homogeneous paper.

Designer / Date: David Mitchell, 2010.

Diagrams: On-line diagrams are available from the Mathematical section of this site.

 
  Name: Squashed Hexagon Tiles

Paper type / shape: Silver rectangles / Any kind of paper.

Designer / Date: David Mitchell, 2000.

Diagrams: As Stretched Hexagon Tiles in Exploring Mathematical Ideas with Origami - Water Trade - ISBN 0953477444 // On-line diagrams are available from the Mathematical section of this site.

 
Single Sheet Polyhedra
 
  Name: Collapsible Cube - square section cube that squashes flat.

Paper type / shape: A4 (cut down to smaller custom rectangle) / Homogeneous paper.

Designer / Date: David Mitchell, 1993

Diagrams: On-line diagrams are available on the Single Sheet Designs page of this site.

 
  Name: Pocket Octahedron - square section tube which collapses into an octahedron.

Paper type / shape: A4 or similar rectangle / Homogeneous paper.

Designer / Date: David Mitchell, 2014.

Diagrams: On-line diagrams are available on the Single Sheet Designs page of this site.

 
  Name: Pocket Tetrahedron - a pure origami version of the traditional pop-up tetrahedron from an envelope.

Paper type / shape: A4 or similar rectangle / Homogeneous paper.

Designer / Date: David Mitchell, 1994.

Diagrams: On-line diagrams are available on the Single Sheet Designs page of this site.

 
  Name: Pocket RhombicTetrahedron - rhombic version of the Pocket Tetrahedron.

Paper type / shape: A4 (cut down to smaller custom rectangle) / Homogeneous paper.

Designer / Date: David Mitchell, 1994.

Diagrams: On-line diagrams are available on the Single Sheet Designs page of this site.

 
  Name: Rhombic Pyramid

Paper type / shape: A4 / Homogeneous paper.

Designer / Date: David Mitchell (based on an idea by David Brill), 1997.

Diagrams: Mathematical Origami - Tarquin Publications - ISBN 1-899618-18-X // In Portuguese - Origami matematicos - Republicao - ISBN 972-570-257-3