Introduction to Crystallography and Mineral Crystal Systems
by Mike and Darcy Howard

Part 9: Conclusion and Further Reading

Well, here we are. We've finished the 6 crystal systems and we're feeling kind of smug with what we have learned. But listen here readers, although we had some chalkboard discussions about the crystal systems and their symmetry elements and classes, now we must leave the ideal world of symmetrical crystal forms and enter the real world. The world where the growth mechanisms and the environment of formation of a crystal have as much to do with the expression of the crystal forms we see as the molecular arrangement of atoms composing the mineral we are interested in.

Almost all minerals are crystalline (part of the definition of a mineral), but only under special conditions do you form minerals with well expressed crystal form(s). The mineral may grow from a melt as in igneous rocks, from solids under elevated temperature and pressure, or in open crevices or pockets from hot, warm, or cold mineral-laden fluids.

So, when you examine euhedral crystals of any mineral, please realize that they are rather remarkable objects. Probably 99 % of all minerals present in the earth's crust display no external crystalline form. A euhedral crystal is a flower of the mineral world! Treat crystals with care and respect because they probably survived millions of years before someone discovered them. One careless moment and they may be destroyed forever.

But enough of our soapbox lecture on the need to understand the scarcity of well-formed crystals! Throughout the series of articles, we have attempted to show you the world of symmetry present in the crystalline world around you. But symmetry is present everywhere. Symmetry is present in varying degrees in the biological world. From simple bilateral symmetry (mirror symmetry like left-right) to 5-fold symmetry not present in the crystalline world. Members of the echinoderm family are beautiful examples of this type of symmetry. Next time you look at a starfish, a fossil blastoid, or a sea urchin spend some time examining its symmetry. You will recognize elements of several principles you learned from studying minerals.

Symmetry or the intentional lack of symmetry governs many artistic works. One of the most remarkable persons to use masterfully a variety of symmetry elements was M. C. Escher. His works not only display many symmetry elements, but he includes much of his personal theology hidden in his designs. An excellent recent book, available by ordering from your local bookstore is M. C. Escher: His Life and Complete Graphic Work, by M. C. Escher, L. J. Locher (ed.), and F. Bool, published by Harry N. Abrams, November, 1992, ISBN: 0810981130. You could also order this book from on the internet. There is a CD-ROM of M. C. Escher's Works also available for less than $50 through

There are many articles written in journals concerned with various aspects of symmetry including an article in Scientific American on the symmetry of the patterns of dimples on golf balls!

One of the most interesting books we ever came across is Snow Crystals by W. A. Bentley and W. J. Humphries.

This remarkable book contains 2,453 photographs of snow crystals (the mineral ice).

W. A. Bentley's hobby was the photography of snow crystals. After his death, his collection of several thousand snow crystal and frost crystal photographs were donated to the American Meteorological Society. The AMS was charged with designating someone to put the collection of photographs into a sensible order and overseeing their publication. W. J. Humphries oversaw the work which involved several noted mineralogists of the day, including S. B. Hendricks, H. E. Merwin, C. S. Ross, and W. T. Schaller. These men classified the photographs into basic types of formation and growth forms and worked up the descriptive portion of the book's text on the crystallography of the Snow Crystal.

The presentation of so many illustrations of a single mineral (ice) all from the same crystal system makes the book unique and gives the viewer the opportunity to examine how the various methods of growth of a mineral may affect a crystal's appearance, even though the symmetry elements remain constant. You have probably heard the comment that no two snow flakes are identical. You will believe it after examining the photographs in this book! Every instructor teaching mineralogy should make this book available to their class just to enlighten the students as to nature's infinite variety on the same theme!

We do not know if it is still in print, but it was first published by McGraw-Hill in 1931 and republished in 1962 by Dover Publications, New York. The standard book number is 486-20287-9 and the Library of Congress Card Catalog Number is 63-422 for the Dover edition.

I could rave on for a few additional pages, but it would do little good. By now, you are either hooked on symmetry or sick of my discussion of it. But never again will you look in a mirror and see just yourself. Instead you will see an organism with bilateral symmetry. Symmetry is a way of looking at the world around you and seeing order in the apparent randomness of nature. It is truly a way to define order out of apparent chaos.

Randomness and chaos are popular topics these days, in mathematics and in philosophical discussions concerning the general nature of life, but I assure you that if you look around and are thinking of symmetry you will find it. It is everywhere in the plant and animal world as well as the mineral kingdom. Just stop, bend down, and look at common clover, a plant whose individual leaves exhibit mirror plane symmetry, but whose 3-leaf arrangement displays trigonal symmetry elements. Think about the symmetry of a 4-leafed clover. Now you are not interested in finding one for good luck, but so you can more thoroughly examine its symmetry!

Speaking of good luck, we wish all of you the best of it in your continuing quest for knowledge. We hope we have brought you to a better understanding and appreciation of the symmetry and beauty of the world around you! For the effort involved in reading all this series, we salute you and you are hereby deserving of the Mineralogical Order of the Crystal Sphere, that one object of infinite symmetry. May the sphere ever remind you of the infinite patience it takes to learn about Crystallography and Geometry.

Mike & Darcy Howard

Index to Crystallography and Mineral Crystal Systems

Table of Contents

Bob Keller