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Paper crystal models

by AuntDaisy

To complement pmoews beautiful collection of 3D printed crystals, Web Mineral has a selection of PDF crystal forms to print on card, cut-out & stick together:

While looking through Evans & Davies' 1924 "Elementary Crystallography", I found an advert for a set of patterns of "Crystal Models".
Here's a scan with a Titanate example : https://lh3.googleusercontent.com/-YiFHzI6WUyo/VWcHe9daPEI/AAAAAAAAAvE/leomNw72Wds/s1320/

7s 6d seems a reasonable price :-)

Sadly, no sign of the patterns on the web...

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Petrie's Infinite Skew Polyhedra

by pmoews

I recently posted models of Petrie and Coxeter's infinite skew polyhedron composed of squares with six square vertices meeting at a point.
https://www.thingiverse.com/thing:2884052 D. Moews pointed out that this arrangement of squares is a member of space group 229 with 6 squares in the repeating unit - It has 2 positions in the unit cell - a in Wyckoff notation - one at 0,0,0 the other at 1/2,1/2,1/2. Point symmetry is m3m.

It seems that Petrie's second infinite skew polyhedron, one where the vertices of four hexagons meet at a point is also a member of space group 229 with four hexagons in the repeating unit.

Coxeter pointed out that there is another infinite polyhedron where the vertices of six hexagons meet at a point. Space Group ?

Comments, Criticisms ?

Models of a Skew Polyhedon
by pmoews
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Measurements on a Quartz crystal

by pmoews

I recently came across a study of a quartz crystal in an out of print book - Crystallography and Practical Crystal Measurements, Volume 1 by AEH Tutton. A reflecting goniometer was used, no xrays, to obtain a complete description of the crystal and the ratio of the unit cell dimensions. I have never seen a reflecting goniometer and found it fascinating. The article starts on p. 462 Chapter 23. Here is a link to a free copy from google - although the book seems to be available from a number of sources.


heres a copy from u michigan which has both volumes and seems searchable


and a lecture on Rock Crystals by AEH Tutton in Vol 88 Nature 1911 p. 261 - 265


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Cubic forms

by pmoews

I very much enjoy Tutton's book on Crystallography and Crystal Measurements. It was published in 1911, a few years before Von Laue showed that x-rays are diffracted by crystals. The mathematics in the book is limited to analytical geometry and Tutton writes clearly. He seems pleased when his measurements agree to within a few minutes of arc.

In particular Chapter XI, on the Cubic System, gives a very thorough explanation of cubic symmetry . There are no equations aside from the calculation of a few angles. Instead he uses stereographic projections and drawings of polyhedra.

It might be easier to follow his discussion if the figures were replaced, where possible, by actual 3 dimensional objects. Having the objects in hand should make it easier to make sense of the stereographic projections. Also the angles could be checked with a protractor.

I've started such a project and hope to complete it shortly. OpenSCAD makes it almost trivial. See:

"Crystallography and Practical Crystal Measurement", AEH Tutton, Macmillan and Co. Ltd, London, 1911, Chapter XI, pages 147 - 171.

The chapter contains 42 Figures.


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