Featured Posts

Feb 2014 / № 11779

overheard-kdu-1

OVERHEARD is a miss-ordered diary of the dark, crude, random and occasionally funny snippets of conversation that I’ve noted down.

For a few years now I’ve taken the nonsense I hear and written it into my phone’s ‘notes’. The quotes – each out of their context – are tagged with the themes of the conversation it was taken from and it’s colour is based on its general category; MIND, AIR and BLOOD. Colour intensity is linked to the time it was written. Every quote has an illustration that embodies its narrative. The snippets are verbatim from my phone (drunken spelling and all).

Read more about the side-project on my site here.

overheard-kdu-2

Sep 2013 / № 11705

The Pantheon

The Pantheon is new personal music and animation project. Curating a new rock’n'roll pantheon of up and coming music stars from the underground UK scenes. Each artist illustrated and animated into simple loops. The first animation of Grime DJ’s and Record Label Butterz (Elijah & Skilliam), who are pushing the vibrant and raw sound of Grime across the globe.

May 2013 / № 11635

15

03

18

16

01

02

17

04

13

12

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

Daniel J Diggle | Twitter

Apr 2013 / № 11619

devour-behance

detail

sketch

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.

Jun 2012 / № 10795

fff-kdu-01

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.

kdu_bullet1Development images here.

― Daniel J Diggle

fff-02

Jun 2011 / № 8332

7b231aad34aed45d988c67c1300f5c0a

3d5e898b16873b0f2749e4c2ab30df71

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”..

kdu_bullet1Development images here.

― Daniel J Diggle


70b97164d58093d7597beac61e39f03a

b35fee5a0687b3684e7370ef0ac8a73b

Apr 2011 / № 7686

thekdu-danieldiggle

DanielDiggle.com/Design

Other than my illustration work, I also work in Digital, designing websites of all flavours and dabbling in other sectors of online too. Bringing all sorts of campaigns to life online and for some great clients, ranging from adidas to Kellogg’s. I’ve a new temp portfolio that’s just gone up. Take a gander just below.

View the design portfolio here.kdu_bullet1

― Daniel J Diggle

Apr 2011 / № 7674

kdu-destroythemachines

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.

kdu_bullet1Development images here.

― Daniel J Diggle

Feb 2011 / № 7183

ca185-final

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.

kdu_bullet1Development images coming soon.

― Daniel J Diggle

ca185-01

ca185-02


Feb 2011 / № 7137

62d75a0aab015bc8e0121258ce032846

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.

kdu_bulletVisit DANIELDIGGLE.COM here.

View development images via flickr.

― Daniel J Diggle

cf5c02f68f1b3372cfa96a8790e88463

roots-dev


Icosidodecahedron
Icosidodecahedron
(Click here for rotating model)
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 CDW dot.pngCDW 5.pngCDW ring.pngCDW 3.pngCDW dot.png
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular
Icosidodecahedron color
Colored faces
Icosidodecahedron
3.5.3.5
(Vertex figure)
Rhombictriacontahedron.svg
Rhombic triacontahedron
(dual polyhedron)
Icosidodecahedron  Net
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.

Contents

[hide]

//

[edit] Area and volume

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

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

[edit] 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:

Uniform polyhedron-53-t0.png
Dodecahedron
Uniform polyhedron-53-t01.png
Truncated dodecahedron
Uniform polyhedron-53-t1.png
Icosidodecahedron
Uniform polyhedron-53-t12.png
Truncated icosahedron
Uniform polyhedron-53-t2.png
Icosahedron

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

Dissected icosidodecahedron.png
(Dissection)
Icosidodecahedron.png
Icosidodecahedron
(pentagonal gyrobirotunda)
Pentagonal orthobirotunda solid.png
Pentagonal orthobirotunda
Pentagonal rotunda.png
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.

Icosidodecahedron.png
Icosidodecahedron
Small icosihemidodecahedron.png
Small icosihemidodecahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Great icosidodecahedron.png
Great icosidodecahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Great icosihemidodecahedron.png
Great icosihemidodecahedron
Dodecadodecahedron.png
Dodecadodecahedron
Small dodecahemicosahedron.png
Small dodecahemicosahedron
Great dodecahemicosahedron.png
Great dodecahemicosahedron
Compound of five octahedra.png
Compound of five octahedra
UC18-5 tetrahemihexahedron.png
Compound of five tetrahemihexahedra

[edit] See also

[edit] 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)

[edit] External links

Jan 2011 / № 6994

kdu-new

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.

kdu_bulletVisit DANIELDIGGLE.COM here.

― Daniel J Diggle

djd-foot


Icosidodecahedron
Icosidodecahedron
(Click here for rotating model)
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 CDW dot.pngCDW 5.pngCDW ring.pngCDW 3.pngCDW dot.png
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular
Icosidodecahedron color
Colored faces
Icosidodecahedron
3.5.3.5
(Vertex figure)
Rhombictriacontahedron.svg
Rhombic triacontahedron
(dual polyhedron)
Icosidodecahedron  Net
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.

Contents

[hide]

//

[edit] Area and volume

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

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

[edit] 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:

Uniform polyhedron-53-t0.png
Dodecahedron
Uniform polyhedron-53-t01.png
Truncated dodecahedron
Uniform polyhedron-53-t1.png
Icosidodecahedron
Uniform polyhedron-53-t12.png
Truncated icosahedron
Uniform polyhedron-53-t2.png
Icosahedron

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

Dissected icosidodecahedron.png
(Dissection)
Icosidodecahedron.png
Icosidodecahedron
(pentagonal gyrobirotunda)
Pentagonal orthobirotunda solid.png
Pentagonal orthobirotunda
Pentagonal rotunda.png
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.

Icosidodecahedron.png
Icosidodecahedron
Small icosihemidodecahedron.png
Small icosihemidodecahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Great icosidodecahedron.png
Great icosidodecahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Great icosihemidodecahedron.png
Great icosihemidodecahedron
Dodecadodecahedron.png
Dodecadodecahedron
Small dodecahemicosahedron.png
Small dodecahemicosahedron
Great dodecahemicosahedron.png
Great dodecahemicosahedron
Compound of five octahedra.png
Compound of five octahedra
UC18-5 tetrahemihexahedron.png
Compound of five tetrahemihexahedra

[edit] See also

[edit] 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)

[edit] External links

Oct 2010 / № 5752

kdu-u-02

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.

kdu_bulletFull development images and process can be viewed here.

― Daniel J Diggle

kdu-process

Icosidodecahedron
Icosidodecahedron
(Click here for rotating model)
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 CDW dot.pngCDW 5.pngCDW ring.pngCDW 3.pngCDW dot.png
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular
Icosidodecahedron color
Colored faces
Icosidodecahedron
3.5.3.5
(Vertex figure)
Rhombictriacontahedron.svg
Rhombic triacontahedron
(dual polyhedron)
Icosidodecahedron  Net
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.

Contents

[hide]

//

[edit] Area and volume

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

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

[edit] 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:

Uniform polyhedron-53-t0.png
Dodecahedron
Uniform polyhedron-53-t01.png
Truncated dodecahedron
Uniform polyhedron-53-t1.png
Icosidodecahedron
Uniform polyhedron-53-t12.png
Truncated icosahedron
Uniform polyhedron-53-t2.png
Icosahedron

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

Dissected icosidodecahedron.png
(Dissection)
Icosidodecahedron.png
Icosidodecahedron
(pentagonal gyrobirotunda)
Pentagonal orthobirotunda solid.png
Pentagonal orthobirotunda
Pentagonal rotunda.png
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.

Icosidodecahedron.png
Icosidodecahedron
Small icosihemidodecahedron.png
Small icosihemidodecahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Great icosidodecahedron.png
Great icosidodecahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Great icosihemidodecahedron.png
Great icosihemidodecahedron
Dodecadodecahedron.png
Dodecadodecahedron
Small dodecahemicosahedron.png
Small dodecahemicosahedron
Great dodecahemicosahedron.png
Great dodecahemicosahedron
Compound of five octahedra.png
Compound of five octahedra
UC18-5 tetrahemihexahedron.png
Compound of five tetrahemihexahedra

[edit] See also

[edit] 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)

[edit] External links

Sep 2010 / № 5322

kdu_01

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.

kdu_bulletWebsite: Wolfbite.co.uk

― Daniel J Diggle

kdu_02

From Wikipedia, the free encyclopedia

Jump to: navigation, search

Icosidodecahedron
Icosidodecahedron
(Click here for rotating model)
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 CDW dot.pngCDW 5.pngCDW ring.pngCDW 3.pngCDW dot.png
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular
Icosidodecahedron color
Colored faces
Icosidodecahedron
3.5.3.5
(Vertex figure)
Rhombictriacontahedron.svg
Rhombic triacontahedron
(dual polyhedron)
Icosidodecahedron  Net
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.

Contents

[hide]

//

[edit] Area and volume

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

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

[edit] 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:

Uniform polyhedron-53-t0.png
Dodecahedron
Uniform polyhedron-53-t01.png
Truncated dodecahedron
Uniform polyhedron-53-t1.png
Icosidodecahedron
Uniform polyhedron-53-t12.png
Truncated icosahedron
Uniform polyhedron-53-t2.png
Icosahedron

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

Dissected icosidodecahedron.png
(Dissection)
Icosidodecahedron.png
Icosidodecahedron
(pentagonal gyrobirotunda)
Pentagonal orthobirotunda solid.png
Pentagonal orthobirotunda
Pentagonal rotunda.png
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.

Icosidodecahedron.png
Icosidodecahedron
Small icosihemidodecahedron.png
Small icosihemidodecahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Great icosidodecahedron.png
Great icosidodecahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Great icosihemidodecahedron.png
Great icosihemidodecahedron
Dodecadodecahedron.png
Dodecadodecahedron
Small dodecahemicosahedron.png
Small dodecahemicosahedron
Great dodecahemicosahedron.png
Great dodecahemicosahedron
Compound of five octahedra.png
Compound of five octahedra
UC18-5 tetrahemihexahedron.png
Compound of five tetrahemihexahedra

[edit] See also

[edit] 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)

[edit] External links

Aug 2010 / № 4784

thekdu_wolfbite

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.

kdu_bulletWebsite: Wolfbite.co.uk

kdu_bulletFacebook: Wolfbite

kdu_bulletTwitter: BittenByWolf

kdu_bulletCreated by: Daniel J Diggle

― Daniel J Diggle

From Wikipedia, the free encyclopedia

Jump to: navigation, search

Icosidodecahedron
Icosidodecahedron
(Click here for rotating model)
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 CDW dot.pngCDW 5.pngCDW ring.pngCDW 3.pngCDW dot.png
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular
Icosidodecahedron color
Colored faces
Icosidodecahedron
3.5.3.5
(Vertex figure)
Rhombictriacontahedron.svg
Rhombic triacontahedron
(dual polyhedron)
Icosidodecahedron  Net
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.

Contents

[hide]

//

[edit] Area and volume

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

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

[edit] 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:

Uniform polyhedron-53-t0.png
Dodecahedron
Uniform polyhedron-53-t01.png
Truncated dodecahedron
Uniform polyhedron-53-t1.png
Icosidodecahedron
Uniform polyhedron-53-t12.png
Truncated icosahedron
Uniform polyhedron-53-t2.png
Icosahedron

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

Dissected icosidodecahedron.png
(Dissection)
Icosidodecahedron.png
Icosidodecahedron
(pentagonal gyrobirotunda)
Pentagonal orthobirotunda solid.png
Pentagonal orthobirotunda
Pentagonal rotunda.png
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.

Icosidodecahedron.png
Icosidodecahedron
Small icosihemidodecahedron.png
Small icosihemidodecahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Great icosidodecahedron.png
Great icosidodecahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Great icosihemidodecahedron.png
Great icosihemidodecahedron
Dodecadodecahedron.png
Dodecadodecahedron
Small dodecahemicosahedron.png
Small dodecahemicosahedron
Great dodecahemicosahedron.png
Great dodecahemicosahedron
Compound of five octahedra.png
Compound of five octahedra
UC18-5 tetrahemihexahedron.png
Compound of five tetrahemihexahedra

[edit] See also

[edit] 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)

[edit] External links

Jun 2010 / № 4271

tiger_beer_new_2

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.

kdu_bulletFull development images and process coming soon…

― Daniel J Diggle

From Wikipedia, the free encyclopedia

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Icosidodecahedron
Icosidodecahedron
(Click here for rotating model)
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 CDW dot.pngCDW 5.pngCDW ring.pngCDW 3.pngCDW dot.png
Symmetry Ih
or (*532)
References U24, C28, W12
Properties Semiregular convex quasiregular
Icosidodecahedron color
Colored faces
Icosidodecahedron
3.5.3.5
(Vertex figure)
Rhombictriacontahedron.svg
Rhombic triacontahedron
(dual polyhedron)
Icosidodecahedron  Net
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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[edit] Area and volume

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

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

[edit] 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:

Uniform polyhedron-53-t0.png
Dodecahedron
Uniform polyhedron-53-t01.png
Truncated dodecahedron
Uniform polyhedron-53-t1.png
Icosidodecahedron
Uniform polyhedron-53-t12.png
Truncated icosahedron
Uniform polyhedron-53-t2.png
Icosahedron

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

Dissected icosidodecahedron.png
(Dissection)
Icosidodecahedron.png
Icosidodecahedron
(pentagonal gyrobirotunda)
Pentagonal orthobirotunda solid.png
Pentagonal orthobirotunda
Pentagonal rotunda.png
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.

Icosidodecahedron.png
Icosidodecahedron
Small icosihemidodecahedron.png
Small icosihemidodecahedron
Small dodecahemidodecahedron.png
Small dodecahemidodecahedron
Great icosidodecahedron.png
Great icosidodecahedron
Great dodecahemidodecahedron.png
Great dodecahemidodecahedron
Great icosihemidodecahedron.png
Great icosihemidodecahedron
Dodecadodecahedron.png
Dodecadodecahedron
Small dodecahemicosahedron.png
Small dodecahemicosahedron
Great dodecahemicosahedron.png
Great dodecahemicosahedron
Compound of five octahedra.png
Compound of five octahedra
UC18-5 tetrahemihexahedron.png
Compound of five tetrahemihexahedra

[edit] See also

[edit] 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)

[edit] External links

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