## Daniel J Diggle

Location:
London, United Kingdom

## Illustrator, designer & amateur writer al'a critique, with a taste for typography, web, motion, print and digital fluff.Opinionated, open-minded, disco dancing on the rave scene, scratchy itchy light englishman.

Daniel James Diggle is a creative working across illustration, print, digital and dabbling with motion. Having worked with a broad spectrum of clients, from adidas, Footlocker, Virgin Money, COI, The Economist, BT, Nesta and more, creative solutions have been produced to help innovate and develop brands and their relationships with the consumer.

Contact / contact{at}danieldiggle.com

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## Pattern

February 2009 / № 107

Some of the patterns I’ve made, exploring working with my stippling based illustrations.

## Devour

February 2009 / № 103

Devour. Illustration created for Depthcore’s latest chapter ‘Primal’. Didn’t quite finish it in time for the cut – but here it is. On Behance too.

## Form Fifty Five

February 2009 / № 100

Form Fifty Five

The first illustration I’ve done in a fair amount of time, a small header piece for the creative blog Form Fifty Five. Warming up the pens for more work this year.

Development images here.

― Daniel J Diggle

## Destroy The Machines

February 2009 / № 094

Destroy The Machines

Depthcore collective have just launched their new chapter “Obsolete” alongside their new website. The piece, Destroy The Machines was re-worked to become part of the chapter. Check out the great Depthcore works here.

The human hands that built their own cage, rise up and strike against the metal bars of their self made oppression. Fighting under one banner and crying in chorus, “Destroy The Machines”..

Development images here.

― Daniel J Diggle

## Destroy The Machines

February 2009 / № 087

Destroy The Machines

Originally started for the latest KDU solstice magazine. Not quite finished in time, I submitted The Roots instead. Now after retrieving the pencil sketch, starting to ink it. I’m using a slightly rougher, more textured approach on this one, fibre tip pens replacing the technical and cross hatching taking up the brunt of the shading. This is a work in progress, check the flickr link below for updates over the coming days.

Development images here.

― Daniel J Diggle

## Computer Arts 185

February 2009 / № 081

Computer Arts

Illustratation created for Computer Arts 185th issue. Through feeding the roots of Inspiration, Technique and Great Design, flourish and bloom creativity. There are two colour versions of the illustration.

Development images coming soon.

― Daniel J Diggle

## The Roots

February 2009 / № 076

The Roots

The Roots, a typographic piece created for the Keystone Design Union. The KDU espouses many masonic ideals and is connected to the Freemasons of New York. Scottish Thistle, Irish Clover, and British and American Roses reflect the entwined historical roots of the Freemasonry organisation.

Visit DANIELDIGGLE.COM here.

View development images via flickr.

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Daniel James Diggle

February 2009 / № 073

DanielDiggle.com

Today I’m launching my new site dedicated solely to my illustration work; collaborations, commissions and personal pieces. New works will be added over the coming weeks, with several new collaborations nearing completion and several commissions due to go up, keep an eye out for updates. For information and collabs, commissions or to request to view my design folio, simply email via the site.

Visit DANIELDIGGLE.COM here.

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Process

February 2009 / № 067

Roots.

For all my illustrations, I like to document the whole process, from initial sketches, notes, experiments and doodlings to the final piece. This was initially born out of a fascination as to how many of my favorite artists created their work and for a process that can be very time consuming, it’s a relief to see where you have come from.

Below are a few shots of a work in progress, my own take on the Keystone Design Union’s logo. Most of my work is half planned half evolving at the time and this piece still has a fair way to go.

A brief rationale: Scottish Thistle, Irish Clover, and British and American Roses reflecting the entwined historical roots of the Masonry organisation – and it’s part in the inspiration/creation of the KDU.

Full development images and process can be viewed

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Slow Growth

February 2009 / № 063

Slow Growth.

“Slow Growth was the first collab between Daniel J Diggle and Jessica Allan. An example of ‘photoshop tennis’ each artist took turns to progressively add to the image, building it up over time.”

Slow Growth, a collab with Jessica Allan and the first complete illustration via the collaboration website Wolfbite.

Website: Wolfbite.co.uk

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Wolfbite

February 2009 / № 060

Wolfbite.

“Wolfbite is the slightly wonkey nail in the plasterboard wall on which to hang the collaborative illustrations we create.”

Web designer and illustrator Daniel J Diggle and fellow illustrator Jessica Allan created Wolfbite as a little home to their creative collaborations and as a place to display future collab’s with other artists too.

Website: Wolfbite.co.uk

Created by: Daniel J Diggle

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Tiger Translate

February 2009 / № 059

Tiger Translate.

A work in progress shot of a piece for Tiger Beers’ Tiger Translate global exhibition. This illustration will be part of a strip of different artworks by artists from West and East, each illustration connecting to the other.

Full development images and process coming soon…

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Gully or Gaza?

February 2009 / № 055

Gully or Gaza?.

A still from a series of animations created for a music and arts event Visual Soundclash. A series of artists and dj’s were paired up, the artists creating the visuals for a 15minute set – the dj’s then battling each other and the crowd deciding the winners. The event was created by Plain Janes and held at C.A.M.P – The City Arts & Music Project.

I was paired with the brilliant muli-creative PC Williams, who’s dancehall/bashment set won through to gain us gold overall.

Video sample via youtube or vimeo.

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Slow Growth

February 2009 / № 047

Slow Growth.

Slow Growth is the first of a series of ongoing collaborations with illustrator Jessica Allan – Taking turns in adding to the illustration, piece-by-piece, the artwork comes together like a spontanious puzzle of mixed elements – a form of photoshop / illustration tennis. This is (as are most things!) a work in progress. These collaborations and others will find their home on the collaboration website Wolfbite ( as and when the gods deem it good to go live that is… ).

Full development images and process can be viewed here.

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

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## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)

## Polyshedron

February 2009 / № 043

Polyshedron.

Polyshedron, illustration work in progress -  polyhedron, icosidodecahedron, cage structures, female form and a hiding sparrow. Final image to be coloured, probably with a watercolour base. Polyhedron spheres decorated with William Morris patterns.

Full development images and process can be viewed here.

― Daniel J Diggle

Icosidodecahedron

Type Archimedean solid
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbol $\begin{Bmatrix} 3 \\ 5 \end{Bmatrix}$
Wythoff symbol 2 | 3 5
Coxeter-Dynkin
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular

Colored faces

3.5.3.5
(Vertex figure)

Rhombic triacontahedron
(dual polyhedron)

Net

A Hoberman sphere as an icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the golden ratio, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

In the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a pentagonal gyrobirotunda.

[hide]

//

## Area and volume

The area A and the volume V of the icosidodecahedron of edge length a are:

$A = (5\sqrt{3}+3\sqrt{25+10\sqrt{5}}) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} (45+17\sqrt{5}) a^3 \approx 13.8355259a^3.$

## Related polyhedra

The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.

The Icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:

 Dodecahedron Truncated dodecahedron Icosidodecahedron Truncated icosahedron Icosahedron

It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.

(Dissection)
 Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda

Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.

## References

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)