Unit Cells in Space or Spaces for Unit Cells
Lawrence C Andrews, Herbert J Bernstein

TL;DR
This paper explores how to define a space for unit cells in crystallography to measure relationships and distances between them.
Contribution
The paper introduces new approaches to represent and measure distances between unit cells in a multidimensional space.
Findings
Unit cells can be represented in a 6-dimensional space using lengths and angles.
A direct metric in this space is not feasible due to incommensurate dimensions.
Alternative 6 or 7-dimensional spaces are proposed for better measurement.
Abstract
Crystallographers think about unit cells as 3 lengths and 3 angles. In other words, as 6 numbers,often in a row. But in order to talk about the relationships between unit cells, we need to know where they are in the space of unit cells, whatever that is. Ideally, we would like to be able to measure the "distances" between 2 or more unit cells, so we would like to have a metric space. The lengths and angles can be treated as a 6- dimensional space, but the they are not commensurate, so there is not a 'nice" measure. Other 6 or 7 dimensional spaces are needed.
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Taxonomy
TopicsModular Robots and Swarm Intelligence
