## Hidden Mathematical Symmetries in the 32 Crystal Point Groups?

**Authors:** Giuliano Bettini

In a preceding paper we introduced a conjecture: the classification of the 32 crystal classes with 5
bits. In the present paper we will review our preceding result, and continue showing some further
interesting issues. In the paper, it is argued that bits should be identified with five basic unknown
symmetries generating these 32 groups. Probably it is not merely a coincidence that 32 means 5
bits. And probably is it not merely a coincidence that each complete subset of bits (properties)
means the holohedry of a crystal system; and each new bit means a new crystal system.
The purpose of this article was of course not to draw a conclusive theory, but to suggest ideas that,
we hope, will be useful for researchers in mathematics, group theory and crystallography.

**Comments:** 10 pages

**Download:** **PDF**

### Submission history

[v1] 16 Jan 2011

**Unique-IP document downloads:** 454 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*