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Feb 2011 / № 7137

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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

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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

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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

Jan 2011 / № 7052

Most of the work in 2010 has been done for editorial and commercial such as Nike Inc.,
Art+Auction Magazine, CEO Magazine and The Prime Russian Magazine.

Click to appreciate it!

Thanks

=(^-^)=

Posted by fiodor Categorized: Design illustration Tags: illustration typography |

UK rock band, To Catch a Thief, approached me about working with them on their new album packaging. They simply provided me with the title and I ran with it and came up with an art direction based on vintage horror films. This is just the cover, the rest of the layout is still in production. More to come later.

Oliver Barrett  |  Cleveland, Ohio  |  http://www.ohbarrett.com |  ohbarrett@ohbarrett.com |  Twitter

Jan 2011 / № 6897

ITSCOOLWHENYOUFREAKONTHEMUSIC
“It’s Cool When You Freak On The Music” – Eric B. & Rakim

Posted by Bram Vanhaeren Categorized: Print Tags: 80's eric B hip hop karim quotes typography |

Jan 2011 / № 6760
Jan 2011 / № 6728


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The KDU x Brooklyn Machine Works x Tokyo

The Keystone Design Union has teamed with legendary independent bike company Brooklyn Machine Works.
Early 2011 will mark the brand relaunch with expanded product range, new website, new collaborations and more.

Dec 2010 / № 6604

Posted by Ato Categorized: Design Print illustration Tags: Ato KDU typography |

HARDER, BETTER, FASTER, STRONGER

Arseny Vesnin (Designcollector) and talented illustrator and iPad monster Fiodor Sumkin (Opera78) started to create the über awesome Digital Magazine “DESIGNCOLLECTOR” Winter 2010/11 for iPad owners.

Illustration below made by Sorin Bechira

DesignCollector Magazine

DesignCollector Magazine

DesignCollector Magazine

Nov 2010 / № 6325

Creative Humans
I’m proud to present you my latest new project, Creative Humans, commissioned by DesignersCouch.org! You can find more information about it on my Behance, for the making, case study, wallpapers and t-shirts you should visit DesignersCouch.

Nov 2010 / № 6192
Nov 2010 / № 6166

I was lucky enough to get featured in the Typoshirt One Book, below are my submissions + featured designs. <3

Typoshirt One Book Feature
Fuck you are so fake

Looks Like it was done by an Art Director

Make Love(tm)

Love Twenty Two

Fashion Love Twenty Two

Featured Design

Featured Design

Featured Design

Photobucket

Photobucket

Photobucket

Photobucket

Photobucket

Photobucket

Photobucket

www.sept-design.com

Posted by sept Categorized: Design Photography Tags: ankhbayar sept septdesign typography |

Nov 2010 / № 6021

A selection of logos, marks and symbols designed by Sorin Bechira from 2005 to 2010.

More details here.

logos makrs symbols

A selection of logos, marks and symbols designed by Sorin Bechira from 2005 to 2010.

More details here.

LoveTwentyTwo© brings you Hello Couture. A collaboration of Fashion and Typography, to promote the important relationship between the many different facets of design.

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