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February 2009 / № 6994



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


(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
(Vertex figure)
Rhombic triacontahedron
(dual polyhedron)
Icosidodecahedron  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.




[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
Uniform polyhedron-53-t01.png
Truncated dodecahedron
Uniform polyhedron-53-t1.png
Uniform polyhedron-53-t12.png
Truncated icosahedron
Uniform polyhedron-53-t2.png

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

Dissected icosidodecahedron.png
(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.

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
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

Toyota Advert / Campaign
I’ve had a huge update. There’s loads of new experimental and commercial illustrative works up on my site now. There’s everything from amazingly complex vector to hyper real psd works for clients around the globe, working with clients as diverse as Bacardi through to Visa. click the title too, there loads more on the full posting or see them all on my site.
February 2009 / № 6826


Playground artwork for KDU in early january. Trust the KDU!

Posted by theyhatemydesign Categorized: The KDU illustration |

February 2009 / № 6750


We just back online in 2011 after slept a long for 2 years. With new love, new works, new passion we stand up today as asian storm. Please visit us and enjoy. Happy Nue Year 2011 for you all. Trust the KDU!

Posted by theyhatemydesign Categorized: Design The KDU Tags: amenth THMD web updates |

February 2009 / № 6630


Vector Calendar 2011 project is brought to you by a few young Artists from Indonesia, and Thmd got a ration making artwork for the month of June. For details to be published in early January 2011. Dont be miss it guys!
Big thx to Heru Prasetyo Jalal for the photos :)

February 2009 / № 6539

staf 005

www.stafmagazine.com //  www.facebook.com/stafmagazine //  www.stafmagazine.tumblr.com

I had the pleasure of having my artwork licensed to be featured on surfable tarps for a Mountain dew commercial. David connected me with the MD people years ago and I have kept in touch for little things here and there. This proved to be a little more than little but the results a trip. I hand drew each of these freestyle, then scanned and auto traced them in illustrator where I added color. BBDO who produced the commercial had them printed into 40×60 foot tarps that Benzo theodore (of jackass notoriety) and Lance Acord (who was the cinematographer on Lost in translation) filmed in Norwalk, CA to make this commercial. Lighthearted but lots of fun.

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Posted by laundry Categorized: Design Photography The KDU Web illustration |

February 2009 / № 6436


Posted by laundry Categorized: Design Press Print The KDU Web illustration |

February 2009 / № 6254


YAW – You Are We

Posted by theyhatemydesign Categorized: Design The KDU illustration |


ACT NOW™ Charity Project | A Tribute to the Victims of Merapi Disaster in my city, Yogyakarta – Indonesia. Model taken from DBH Templete.

February 2009 / № 6209


We at Laundry! recently completed this animated film for Levi’s showcasing their Trucker jacket collaborations with Opening Ceremony, Neighborhood/Stussy, Billy Reid, Filson and Pendington. Our concept was to create a world made of denim where a single character wearing the collaboration jacket exists within the environment where the partnering jacket company is from, NY, LA, Alabama, New Mexico and Oregon. We built this entire animation with stop motion of the jackets and stills of denim put together in adobe after effects to create a fake sense of dimension. See below for the film.

February 2009 / № 6173

I finally put together a personal site for my design and illustration work with hopes of pushing the less commercial side creatively and highlighting the less corporate side of my body of design.


February 2009 / № 6090



Produced for the KDU/
More details soon.

Posted by Gabriel Pulecio Categorized: Design KDU The KDU Tags: Art Gabriel Pulecio Lustix |

February 2009 / № 5909

A set of colorways for a new Laundry! board design we are putting out for the winter.


Posted by laundry Categorized: Design Press Print The KDU illustration |

We had the pleasure at Laundry! of throwing in our two cents typographically for Will.i.ams new video feat. the ever unique Nicki Minaj which was our main reason for taking this on. The concept was to visually nod to korean game shows and their frenetic rediculousness and pair that with both Will and Nicki’s spastic delivery. We have no idea what the words say, we are told they are close translations. Click here to see more of our work.


YouTube Preview Image



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