Origami Heaven A paperfolding
paradise
The website of
writer and paperfolding designer David Mitchell
x


Modular
Polyhedra  FlatFaced Designs 

There is a separate page for
Flat faced Cubes and Silverhedra 

Deltahedra 

I use the term deltahedra to
refer to solids whose faces are all equilateral
triangles. 

Regular
Tetrahedra 



Name: MirrorImage
Tetrahedron Modules / Paper
shape / Folding geometry: 2 mirrorimage modules
from double bronze rectangles using 60/30 degree
folding geometry.
Designer /
Date: David Mitchell, 1996.
Reference:
131
Diagrams:
Mathematical Origami  Tarquin Publications 
ISBN 189961818X // In Portuguese  Origami
matematicos  Republicao  ISBN 9725702573





Name: Robust MirrorImage
Tetrahedron Modules / Paper
shape / Folding geometry: 2 mirrorimage
equilateral modules from bronze rectangles using
60/30 degree folding geometry.
Designer /
Date: David Mitchell, 1998
Reference:
162
Diagrams:
Not yet available.





Name: Variable Tetrahedra.
The positions of the flaps and pockets can be
varied to create five tetrahedra, all of
identical appearance, but each made from a
different combination of modules. Modules / Paper
shape / Folding geometry: 2 modules from bronze
rectangles using 60/30 degree folding geometry.
Designer /
Date: David Mitchell, 2017
Reference:
575
Diagrams:
As Regular Tetrahedra in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169





Name: Striped MirrorImage
Tetrahedron Modules / Paper
shape / Folding geometry: 2 mirrorimage Abe or
Terada modules or the equivalent geometry
embedded in squares. 60/30 degree folding
geometry.
Designer /
Date: David Mitchell, 2003.
Reference:
534
Diagrams:
Not yet available.





Name: Quartetra
 four part modular assembly puzzle. Paper type / shape:
Hexagon / Any kind of paper.
Designer /
Date: David Mitchell, 1988.
Reference:
030
Diagrams:
Paperfolding Puzzles  Water Trade  ISBN
095347740X // Paperfolding Puzzles (2nd Edition) 
David Mitchell  Water Trade  ISBN
9780953477456





Name: Reptile
Tetrahedron Modules / Paper
shape / Folding geometry: 12 Reptile modules from
squares using 60/30 degree folding geometry.
Designer /
Date: David Mitchell, 1997.
Reference:
146
Diagrams:
BOM 189 April 1998 // Online diagrams are
available on the Modular Designs page of this site.





Name: 12part Tetrahedron Modules / Paper
shape / Folding geometry: 12 modules from silver
rectangles using 60/30 degree folding geometry.
Designer /
Date: David Mitchell,1991.
Reference:
081
Diagrams:
In BOS Convention Pack Spring 1992.



Equilateral
Hexahedra 



Name: Robust
Diamond Hexahedron Modules / Paper
shape / Folding geometry: 6 equilateral modules
in 2 sets of 3 mirrorimage versions folded from
bronze rectangles using 60/30 degree folding
geometry.
Designer /
Date: David Mitchell, 2017.
Reference:
162
Diagrams:
As Diamond Hexahedron in Mathematical Origami  David Mitchell 
Tarquin publications  ISBN 9781911093169



Regular
Octahedra and other Deltahedral BiPyramids 



Name: Robust
Triangular Equilateral BiPyramid Modules / Paper
shape / Folding geometry: 3 equilateral modules
folded from bronze rectangles using 60/30 degree
folding geometry.
Designer /
Date: David Mitchell, 2017.
Reference:
162
Diagrams:
As Triangular Equilateral BiPyramid in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169





Name: Regular
Octahedron (2part). Not robust. Modules / Paper
shape / Folding geometry: 2 modules folded from
double bronze rectangles using 60/30 degree
folding geometry.
Designer /
Date: David Mitchell, 1997.
Reference:
144
Diagrams:
Mathematical Origami  Tarquin Publications 
ISBN 189961818X // In Portuguese  Origami
matematicos  Republicao  ISBN 9725702573





Name: Robust
Octahedron Modules / Paper
shape / Folding geometry: 4 equilateral modules
folded from bronze rectangles using 60/30 degree
folding geometry.
Designer /
Date: David Mitchell, 1998.
Reference:
162
Diagrams:
As Regular Octahedron in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169





Name: Robust
Pentagonal Equilateral BiPyramid Modules / Paper
shape / Folding geometry: 5 equilateral modules
folded from bronze rectangles using 60/30 degree
folding geometry.
Designer /
Date: David Mitchell, 2017.
Reference:
162
Diagrams:
As Pentagonal Equilateral BiPyramid in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169



Regular
Icosahedra 



Name: Robust
Icosahedron Modules / Paper
shape / Folding geometry: 10 equilateral modules
in 2 sets of 5 mirrorimage versions folded from
bronze rectangles using 60 degree folding
geometry.
Designer /
Date: David Mitchell, 1998.
Reference:
162
Diagrams:
As Regular Icosahedron in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169





Name: Striped
MirrorImage Icosahedron  can be made
from Abe or Terada modules or from the equivalent
designs embedded in squares. Modules / Paper
shape / Folding geometry: 10 modules in 2 sets of
5 mirrorimage versions folded from bronze
rectangles or squares using 60/30 degree folding
geometry.
Designer /
Date: Modules  Various. Assembly  David
Mitchell, 2003.
Reference:
Diagrams:
Not yet available.



The
Equilateral Dodecahedron 



Name: The
Robust Equilateral Dodecahedron Modules / Paper
shape / Folding geometry: 6 equilateral modules
in 2 sets of 3 mirrorimage versions folded from
bronze rectangles using 60 degree folding
geometry.
Designer /
Date: David Mitchell, 2017.
Reference:
162
Diagrams:
As the Equilateral Dodecahedron in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169



The
Equilateral Hexakaidecahedron 



Name: The
Robust Equilateral Hexacaidecahedron Modules / Paper
shape / Folding geometry: 8 equilateral modules
in 2 sets of 4 mirrorimage versions folded from
bronze rectangles using 60 degree folding
geometry.
Designer /
Date: David Mitchell, 2017.
Reference:
162
Diagrams:
As Equilateral Hexacaidecahedron in Mathematical Origami  David Mitchell 
Tarquin publications  ISBN 9781911093169



The
Equilateral Heccaidecahedron 

Details not yet available. 

Regular
Dodecahedra 



Name: Regular
Dodecahedron  fullface module version
 not robust. Modules / Paper shape / Folding
geometry: 12 modules from squares using mock
platinum folding geometry.
Designer /
Date: David Mitchell, 1996.
Reference:
126
Diagrams:
Mathematical Origami  Tarquin Publications 
ISBN 189961818X // In Portuguese  Origami
matematicos  Republicao  ISBN 9725702573





Name: Robust
Dodecahedron. Versions only differ in
paper shape used. Version 1: Faces
stand slightly proud.
Modules /
Paper shape / Folding geometry: 30 modules from
silver rectangles.
Designer /
Date: David Mitchell, 1992. Possibly invented at
an earlier date by David Brill.
Reference:
576
Diagrams:
Not published.
Version
2: Flat faces.
Modules /
Paper shape / Folding geometry: 30 modules from
mock platinum rectangles.
Designer /
Date: David Mitchell, 2016.
Reference:
576
Diagrams:
As Regular Dodecahedron in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169



Rhombic
and SemiRhombic Polyhedra 

When I
was writing the first edition of my book, Mathematical
Origami, I found that I wanted to include several
polyhedra for which there did not appear to be an
established mathematical name. The characteristics of
these polyhedra were that their faces were either
109.28/70.32 rhombuses or 70.32/54.84/54.84
(1:sqrt3/2:sqrt3/2) triangles, which can be obtained by
folding the 109.28/70.32 rhombus in half lengthways, or a
mixture of the two. For want of better, I stole the word
'rhombic' from the name of the rhombic dodecahedron,
whose faces are, of course, 109.28/70.32 rhombuses, and
applied it to the other polyhedra as well, thus creating
the terms rhombic tetrahedron, rhombic octahedron etc and
the general term rhombic polyhedra to describe them as a
group. I justified this usage to myself on the grounds
that the triangular faces occurred in pairs, which if
flattened would come back to a 109.28/70.32 rhombus.
Somewhat to my surprise, my publisher raised no objection
to this.
I was expecting
that I would receive a barrage of criticism for this
usage and that someone would soon point out to me a
better terminology to use for these forms, but, so far,
neither of these things have happened. I still, however,
expect a better terminology to emerge at some stage.
Pro tem then I
shall continue to use the term rhombic polyhedra,
although in a slightly developed sense, to mean the set
of those polyhedra which can be combined with other
identical polyhedra to build a rhombic dodecahedron and
which have at least some faces that are either
109.28/70.32 rhombuses or 70.32/54.84/54.84
(1:sqrt3/2:sqrt3/2) triangles. The members of this
interesting set of polyhedra are illustrated below. All
of them will fill space.
This definition
deliberately excludes many polyhedra whose faces are
70.32/54.84/54.84 (1:sqrt3/2:sqrt3/2) triangles, and
particularly those that can be made by putting together
threesided pyramids, or sunken pyramids, whose faces are
such triangles and similar designs whose faces are or
include 109.28/35.36/35.36 (sqrt2:sqrt3/2:sqrt3/2)
triangles, which can be obtained from the 109.28/70.32
rhombus by folding it in half in the other direction. If
these forms were to be included within the definition of
rhombic polyhedra then we would be in a situation where
there were, for instance, three separate forms that could
quite correctly be called rhombic hexahedra and three
more that could quite correctly be called rhombic
dodecahedra. This is clearly nonsensical and so I have
adopted the narrower definition given above. I have not
invented any general name for the excluded forms.
It is worth
pointing out that although the 109.28/70.32 rhombus has
diagonals in the proportion 1:sqrt2 I have avoided using
the term silver rhombus since that would suggest that
this rhombus has properties similar to the silver
rectangle and silver triangle, which it does not.
The classic book
Mathematical Models, by H M Cundy and A P Rollett
contains a net for the rhombic pyramid, although the
authors do not give it a name. They do, however, use the
term rhombic polyhedra in a different sense from mine as
a general term for polyhedra whose faces are rhombuses,
ie the cube, the rhombic dodecahedron and the
triacontahedron. I apologise for introducing confusion by
using this term in another way.
The third edition
of this book, published in 1960, also contains the
information that a Mr Dorman Luke, otherwise unknown to
me, has found that all three stellations of the rhombic
dodecahedron can be arrived at by adding what I call
rhombic pyramids to the rhombic dodecahedron in
successively larger numbers. These forms fall outside my
definition of rhombic polyhedra but this is not a
difficulty as they already have their own established
names. I have, incidentally, found that by continuing the
process of adding rhombic pyramids to the third
stellation it is eventually possible to arrive at a much
larger rhombic dodecahedron than the one used to initiate
the process.


Rhombic
and SemiRhombic Tetrahedra 



Name: The MirrorImage
Rhombic Tetrahedron. Modules / Paper
shape / Folding geometry: 2 mirrorimage modules
folded from silver rectangles.
Designer /
Date: David Mitchell, 1996.
Reference:
129
Diagrams:
Mathematical Origami  Tarquin Publications 
ISBN 189961818X // In Portuguese  Origami
matematicos  Republicao  ISBN 9725702573





Name: The Robust
MirrorImage Rhombic Tetrahedron. Modules / Paper
shape / Folding geometry: 2 mirrorimage
truncated Robinson modules folded from silver
rectangles.Three versions possible as the set of
modules can be configured and assembled in three
different ways.
Designer /
Date: David Mitchell, 1998.
Reference:129
Diagrams:
Diagrams not yet available.





Name: The Variable Rhombic
Tetrahedron Modules / Paper
shape / Folding geometry: 2 modules from double
silver rectangle strip. Three versions possible
as the set of modules can be configured and
assembled in three different ways.
Designer /
Date: David Mitchell, 2017
Reference:
545
Diagrams:
Diagrams not yet available.





Name: Pocket Rhombic
Tetrahedron Modules / Paper
shape / Folding geometry: 2 modules from 1x3/4
silver rectangles using silver rectangle
geometry.
Designer /
Date: David Mitchell, 1994.
Reference:
113
Diagrams:
Diagrams not yet available.





Name: The Variable Rhombic
Tetrahedron. The positions of the flaps
and pockets can be varied to create five
tetrahedra, all of identical appearance, but each
made from a different combination of modules. Modules / Paper
shape / Folding geometry: 2 mirrorimage modules
folded from silver rectangles.
Designer /
Date: David Mitchell, 2017.
Reference:
Diagrams:
As the Rhombic Petrahedron in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169.





Name: The Semi Rhombic
Tetrahedron Modules / Paper
shape / Folding geometry: 2 modules folded from
silver rectangles.
Designer /
Date: David Mitchell, 2017.
Reference:
547
Diagrams:
In Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169



Rhombic
Hexahedra 



Name: The Rhombic Hexahedron
 replihedron which is one third of a
rhombic dodecahedron. Modules / Paper
shape / Folding geometry: 2 modules folded from
silver rectangles.
Designer /
Date: David Mitchell, 2004.
Reference:
268
Diagrams:
Diagrams not yet available.





Rhombic
Octahedra 



Name: The Assymetric Rhombic
Octahedron Modules / Paper
shape / Folding geometry: 2 modules folded from
silver rectangles.
Designer /
Date: David Mitchell, 2004.
Reference:
266
Diagrams:
Diagrams not yet available.





The
Rhombic Pyramid, the SemiRhombic Pyramid and the Square
Base Rhombic Pyramid 



Name: The
2part Rhombic Pyramid Modules / Paper
shape / Folding geometry: Made by combining a
rhombic fourpockets module with a rhombic hat /
Both folded from silver rectangles.
Designer /
Date: David Mitchell, 2000.
Reference:
147
Diagrams:
In Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169





Name: The Square
Base Rhombic Pyramid Modules / Paper
shape / Folding geometry: 4 modules from silver
rectangles.
Designer /
Date: David Mitchell, 2017.
Reference:
543
Diagrams:
In Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169



Rhombic
Dodecahedra 



Name: Kite
Pattern Rhombic Dodecahedron Modules / Paper
shape / Folding geometry: 24 modules from silver
rectangles.
Designer /
Date: David Mitchell, 1990.
Reference:
067
Diagrams:
Online diagrams are available on the Modular Designs page of this site.





Name: David
Mitchell's Rhombic Dodecahedron (so
named to distinguish it from Nick Robinson's
Rhombic Dodecahedron, from which it is derived). Modules / Paper
shape / Folding geometry: 12 rhombic triangle
modules folded from silver rectangles.
Designer /
Date: David Mitchell, 2004.
Reference:
267
Diagrams:
In Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169



The
First Stellated Rhombic Dodecahedron 



Name: 6part
Stellated Rhombic Dodecahedron Modules / Paper
shape / Folding geometry: 6 modules from silver
rectangles using silver rectange folding
geometry.
Designer /
Date: David Mitchell, 1989.
Reference:
042
Diagrams:
Reviewed in BOM 139 December 1989 // Wonderful
World of Modulars  Tomoko Fuse  4405075530 
published in Japanese // BOS Convention Pack
Autumn 1989  diagrams drawn by Francis Ow //
Photo on Gallery section of Origami: The Complete
Guide to the Art of Paperfolding  Rick Beech 
Lorenz Books (Anness Publishing)  ISBN 075480782
// Photo on cover of Russian Origami Society
magazine issue 3 1999 // Orison 6 2009 // Also in
Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169 // Online diagrams are available
on the Modular Designs page of this site.





Name: 24part
Stellated Rhombic Dodecahedron  made by
adding 'hats' to Nick Robinson's Rhombic
Dodecahedron. Modules / Paper shape / Folding
geometry: 24 modules in two sets of twelve from
silver rectangles using silver rectangle folding
geometry.
Designer /
Date: David Mitchell, 1997.
Reference:
150
Diagrams:
Mathematical Origami  Tarquin Publications 
ISBN 189961818X // In Portuguese  Origami
matematicos  Republicao  ISBN 9725702573 //
Quadrato Magico 101 Autumn 2011



Other
FlatFaced Polyhedra 



Name: The
Robust Diamond Hexahedron Modules / Paper
shape / Folding geometry: 6 equilateral modules
in 2 sets of 3 mirrorimage versions folded from
bronze rectangles using 60 degree folding
geometry.
Designer /
Date: David Mitchell, 2017.
Reference:
Diagrams:
As the Diamond Hexahedron in Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169





Name: The
Square Base Equilateral Pyramid Modules / Paper
shape / Folding geometry: 4 modules from
silverdouble bronze rectangles using 60 degree
folding geometry.
Designer /
Date: David Mitchell, 2017.
Reference:
Diagrams: Mathematical Origami (2nd Edition) 
David Mitchell  Tarquin publications  ISBN
9781911093169





Name: Compound of Cube and
Octahedron  made by adding hats to the
Twisted Square Cube. 12 squares. Modules / Paper
shape / Folding geometry: 6 modules from squares
using standard folding geometry and 6 from
squares using 60/30 degree folding geometry..
Designer /
Date: David Mitchell, 2016.
Reference:
541
Diagrams:
Not yet available.





Name: Great
Dodecahedron Modules / Paper
shape / Folding geometry: 12 modules from
pentagons.
Designer /
Date: David Mitchell, 1990.
Reference:
061
Diagrams:
Diagrams not yet available.





Name: Small
Stellated Dodecahedron (30part) Modules / Paper
shape / Folding geometry: 30 modules from squares
using mock platinum folding geometry.
Designer /
Date: David Mitchell, 1990.
Reference:
536
Diagrams:
Diagrams not yet available.





Name: Small
Stellated Dodecahedron (60part) 
Design from squares that allows each of the
pentagrams visible on the surface of the form to
be made from paper of a different colour. Modules / Paper
shape / Folding geometry: 60 modules from squares
using mock platinum folding geometry.
Designer /
Date: David Mitchell, 2016.
Reference:
537
Diagrams:
Online diagrams are available on the Modular Designs page of this site.





Name: Spiky
Star Modules / Paper shape / Folding
geometry: 30 modules from 2x1 rectangles using
standard rectangle folding geometry.
Designer /
Date: David Mitchell, 2001.
Reference:
238
Diagrams:
Diagrams not yet available.





Name: Kite
Pattern Triacontahedron Modules / Paper
shape / Folding geometry: 60 modules from custom
rectangles using golden rectangle folding
geometry.
Designer /
Date: David Mitchell, 1990.
Reference:
068
Diagrams:
Online diagrams are available on the Modular Designs page of this site.



