Genus: 3

Symmetry: Multi-layored

The {5,5} is one of my most recent and surprising discoveries. I'd looked in vien for a {5,4} and had all but given up on finding an infinite polyhedra composed of pentagons. Almost as a lark I tried with five at a vertex and very quickly found the above configuration. I would be surprised if there are any others. I later learned that this figure had been previously discovered and published by J. Richard Gott III in 1967. It's interesting to note that Gott is an astronomer who is currently looking for evidence that the universe may exist in a finite, repeating space such as the one in which this model is described.

Main Infinite Regular Polyhedra page.

Superliminal home page.