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

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.

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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)