It's a 2d projection of a rhombic hexecontahedron, first generated by Mathematica's namesake programming language back in the 1980s, when it was as damned close to magic as anything in computer science.
Spikey is one of my favorite logos. They went through many variations with many products, inspired by renaissance drawings and a vast selection of other influences, on their way to the one you see here, which was originally devised for Wolfram Alpha.
Founder Stephen Wolfram:
And that's when I noticed an email from June 2009, from an artist in Brazil named Yolanda Cipriano. She said she'd seen an article about Wolfram|Alpha in a Brazilian news magazine—and had noticed the Spikey—and wanted to point me to her website. It was now more than nine years later, but I followed the link anyway, and was amazed to find this:
Yolanda Cipriano's website—with rhombic hexecontahedra, there called "giramundos"
I read more of her email: "Here in Brazil this object is called 'Giramundo' or 'Flor Mandacarú' (Mandacaru Flower) and it is an artistic ornament made with [tissue paper]".
What?! There was a Spikey tradition in Brazil, and all these years we'd never heard about it? I soon found other pictures on the web. Only a few of the Spikeys were made with paper; most were fabric—but there were lots of them
The Story of Spikey [blog.stephenwolfram.com]