Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

x

 
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.
 
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.

 
Tiles and polygons
 
  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.

 
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