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PhotosNot tetrahexahedron

5th Jan 2022 19:59 UTCJohan Kjellman Expert

Pyrite

Glageon Quarry (Le Cailloit Quarry), Glageon, Avesnes-sur-Helpe, Nord, Hauts-de-France, France

I was searching for images with tetrahexahedra, and this image came up.

This is rather a trapezohedron - {311} maybe?

cheers

6th Jan 2022 08:22 UTCLukáš Křesina

You are right, it is not tetrahexahedron. And it is {311} or even {411}, but it is called tetragonal trisoctahedron, not trapezohedron.

Lukáš Křesina

6th Jan 2022 09:02 UTCFrank K. Mazdab 🌟 Manager

Either name is correct..."isometric trapezohedron" is the traditional name, and "tetragon trisoctahedron" is the modern international name. Since there are also trapezohedrons in other crystal systems (and these have their own prefixes), adding the isometric prefix is helpful, although admittedly I'm not sure I've ever seen anybody actually bothering to do that when describing this common form in garnets, leucite or analcime.

6th Jan 2022 10:25 UTCLukáš Křesina

Frank, thanks for your clarification. It seems czech crystalographical terminology is very modern :-).

Lukáš Křesina

6th Jan 2022 10:10 UTCal kimik

found that https://www.researchgate.net/profile/Walter-Franke/publication/275032549/figure/fig5/AS:294463168630806@1447216898603/a-Tetrahexahedron-hk0-formed-at-100-C-upon-etching-with-1-M-AlCl-3-th-1-M-NH-4-Cl-pH.png

6th Jan 2022 11:07 UTCJosé Zendrera 🌟 Manager

To me these form are deltoidal icositetrahedrons.

https://en.wikipedia.org/wiki/Deltoidal_icositetrahedron

Not most frequent {211} but {311} or {411} as said.

Seems there is a mess here...

6th Jan 2022 14:00 UTCJohan Kjellman Expert

I don't think there is a mess. Just, firstly, nomenclature of different aspects and traditions, and, secondly, general to more specific nomenclature.

I think we all agree that it is a trapezohedron (has trapezohedral faces) it is also an icositetrahedron (has 24 faces as also the tetra[kis]hexahedron).

But is it really (also) a deltoidal icositetrahedron? I may be wrong but doesn't that just refer to the very specific form {211}? At least that is the impression I get from reading the wikipedia-link.

cheers

6th Jan 2022 21:58 UTCJosé Zendrera 🌟 Manager

Johan, I said a mess in the sense that in the mineral world we all understand what a trapezohedron is and have in mind the image of a {211} form of the isometric system. But Wikipedia and geometry sites have another concept of trapezohedron: https://mathworld.wolfram.com/Trapezohedron.html
It is true that Wikipedia is not clear about deltoidal icositetrahedron varieties but I suppose it includes any form with 24 faces, 26 vertex and 48 edges

Anyway description of these amazing pyrite photos should be revised for tetrahexahedron mistake and its wrong assumption to {120} form, which corresponds to pyritohedron. Also size or FOV should be specified.

6th Jan 2022 22:42 UTCJohan Kjellman Expert

Jose,

As I understand it - trapezohedron is a general name, if we stick to the isometric/cubic system, it incorporates {211}, {311},...{hll}. Even more generally it incorporates any polyhedron enclosed by identical trapezohedral faces.

Regarding the Wikipedia-link to the deltoid icositetrahedron and its synonyms it says that the form in geometry "is a Catalan solid" and that it is the dual of the rhombicubeoctahedron. To me, this suggests that it is a "fixed form", and the fact that there are precise angles etc. describing it confirms that. Furthermore, I am now not even certain that integer Miller indices, i.e. rational numbers, suffice to describe it.

Unfortunately, I am neither crystallographer, geometrician nor mathematician enough to resolve this matter.

cheers

6th Jan 2022 13:54 UTCHarold Moritz 🌟 Expert

A trapezohedral form that isn't the common {112}. There are various angles of inclination this form can show, according to Manual of Mineralogy.

6th Jan 2022 14:45 UTCMark Holtkamp

Goldschmidt's Atlas der Krystallformen lists about 27 trapezohedra for pyrite, Kostov & Kostov states there are 60. But the trapezohedron seems to be very rare as a dominant form, I browsed Goldschmidt's drawings an saw only about 10, and only one with {311} as the dominant form, and also only one with {411} as dominant form. These crystals are from a limestone quarry near Franklin Furnace.

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