A dodecahedron approximates a sphere more closely than any other Platonic polyhedron. This gives it a number of useful characteristics. It's the most compact shape and has the smallest internal distances. Since it consists entirely of regular pentagons, it's fairly easy to mass produce.

Computer
hardware components tend to be two-dimensional, although they can be slotted together to occupy much of a three-dimensional space. On a microscopic scale, it's difficult to create cube-shaped integrated circuits, so the third dimension is hard to use.

If circuit boards and integrated circuits were constructed as dodecahedra, this would have several advantages. It would be possible to pack more components into the same space and signalling could be faster because the distances between the components would be smaller than if arranged at right angles on a plane. If the signal has to cross an "empty" space between two faces on a dodecahedral circuit board, use a laser and a photocell.

So, i envisage a computer whose motherboard consists of twelve pentagons with edge connectors and slots on the edges, studded with lasers and photocells. The components themselves are also dodecahedral, covered in sensors and lasers and fit into pentagonal slots on the faces. Some communication is by lines on the surfaces, some by light. This would also enable parts of the motherboard to be upgraded easily by removing individual faces.

There may be an overheating issue, because dodecahedra have relatively small surface areas. I propose to solve this by making the boards porous, placing a number of pinholes in the integrated circuit packages and bathing the whole lot in liquid nitrogen. If that turned out to be too turbulent for the light to work properly, i would make it slightly warmer and suffuse the interior of the case with nitrogen just above boiling point.

Roman Dodecahedronhttp://en.wikipedia.../Roman_dodecahedron Clearly they had a function at some point, but no-one now knows what. [nineteenthly, Oct 23 2008]

Icosahedra are less "spherical". Assuming lines on the faces to form secants at midpoints between the centres and the edges, the volume of a sphere is closer to a dodecahedron than an icosahedron, or at least i think so, but it's been years since i thought about it in detail. An icosahedron would also have more weak spots - more edge connectors and slots to fail. Whereas the pentagon isn't as easy to make as a rectangle or equilateral triangle, it's easier than putting miniaturised components onto a sphere because that would involve rotating the whole sphere rather than moving along a plane. I think a plane can be kept at a fixed distance more easily than the surface of a sphere.

If you put the heat-dissipating components on the external surfaces, with big heatsinks, and all the communications on the inside, you could probabably get away without the LN2.

If you use transparent circuit boards and use visible lsers internally, it would look very pretty in operation, too. [+]

//Icosahedra are less "spherical". // Well they are a closer approximation to the incribed sphere, whilst the dodecahedron is the closest approximation to the circumscribed sphere. You want to interface different planes of your solid so I think you want to consider the inscribed sphere.

//An icosahedron would also have more weak spots - more edge connectors and slots to fail.// Not so. For 20 faces you have 30 edges and 12 vertices (icosahedron). For 12 faces you have 30 edges and 20 vertices (dodecahedron).

//I think a plane can be kept at a fixed distance more easily than the surface of a sphere.// Not if that fixed point is the origin, or "gravicentre". Although this has nothing to do with anything here.

This is more a tiling problem than anything alse. Why not contemplate geodesic domes?

Yes, geodesic domes are a possibility but i am desperate for an application for the pretty pretty dodecahedron, oh, and the circuit boards should be both transparent and violet.

I agree *something* ought to be done with the "dodo" - even in Dungeons & Dragons that most intriguing of dice was hardly ever used. There was like one weapon that used it for damage; that was it. The awkward, phony d10 die was used much more often.

I don't really understand the idea but I would have thought that a space-filling polyhedron, such as the rhombic dodecahedron, is what you're after. Space-filling polyhedra have the advantage that the faces of adjacent cells are parallel, thus making communication between them easier.

The idea is to make hardware which is modular, compact and minimises the distances between the components, both on the motherboard level and that of integrated circuits. It would be expensive, mainly because of the number of lasers needed. A rhombic dodecahedron would be just the thing, but there are also aesthetic criteria, and the "moral" one of not neglecting the regular dodecahedron, which i feel is naturally and technologically underused. A regular one would still have six sets of parallel faces. [phundug], that's most unfortunate. I'd always thought RPGs were one area where dodecahedra could frolic and reach their full potential, what with Wumpus and all that as well.