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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

DanielDiggle.com | Flickr


February 2009 / № 073

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

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[edit] 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.

[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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