Eric Weisstein

What’s in the Logo? That Which We Call a Rhombic Hexecontahedron

May 19, 2009 —

Every aspect of Wolfram|Alpha has been thought through in great detail. Its logo is no exception.

As a tip of the hat to the vast and powerful computational engine that powers Wolfram|Alpha, a natural place to start brainstorming for an appropriate logo was in Mathematica itself. And this is where I, geometry enthusiast and the developer of the PolyhedronData computational data collection, came into the picture.

As many of you may know, Mathematica‘s logo is a three-dimensional polyhedron affectionately called “Spikey.” In its original (Version 1) form, Spikey consisted of the spiked solid obtained from an icosahedron (the regular 20-faced solid that is one of the five Platonic solids) with regular tetrahedra (triangular pyramids) affixed to its faces.

Mathematica Version 1 Spikey

More elaborate forms of Spikey were used in each subsequent version of Mathematica. The current Spikey is an embellishment of a so-called hyperbolic dodecahedron (basically, a regular dodecahedron whose faces become special curved surfaces according to fixed mathematical rules). For a very interesting account of how the current-generation Spikey was created, see the fascinating Wolfram Blog post by Michael Trott.

Mathematica Version 7 Spikey

For Wolfram|Alpha, we wanted a simple yet elegant polyhedral logo that harked back to Spikey (yet retained its own intrinsic uniqueness), was geometrically interesting, and was visually attractive. We considered hundreds of possibilities, including many from my rather extensive collections of polyhedra on MathWorld and PolyhedronData. After rejecting many candidates, we finally settled on the attractive solid known as the rhombic hexecontahedron (“rhombic” refers to the fact that the faces of the solid consist of rhombi, while “hexecontahedron” is a word derived from the Greek, which simply means “60-faced solid”).

Wolfram|Alpha Logo

The rhombic hexecontahedron is a polyhedron that can be obtained as one of the 227 “fully supported” rhombic triacontahedron stellations. (For more details on the rhombic triacontahedron and the process of stellation, the reader is referred to MathWorld). It turns out that this solid has a number of very interesting mathematical properties, including several relations to the famous golden ratio. To explore some of the solid’s properties, see Sándor Kabai’s “Inside the Rhombic Hexecontahedron” example at the Wolfram Demonstrations Project. Rather surprisingly, this solid is actually inferred to exist in nature as the central core of a quasicrystal aggregate of Al6Li3Cu produced by slow solidification.

Of course, the real fun of Wolfram|Alpha is not what’s in its name or its logo, but rather in what it can do. My colleagues and I have been working very hard for nearly three years to make sure that it includes many interesting and useful things, one small part of which (as you might expect) is the ability to compute and display properties and images of many polyhedra (not to mention a few other mathematical objects).

With so much in the universe left to compute, we know there are years of refinements, additions, and enhancements that will follow the initial release of Wolfram|Alpha. So, as the site continues to grow and move forward, it’s likely that its logo will continue to reflect this growing sophistication in some small measure. Which I think is a nice touch. Even though the site would be just as sweet under any other logo.