Re: dome vs. sphenoid
Greetings,
I see that the old confusion dome/sphenoid comes back again. The geometric eigensymmetry cannot differentiate between the two: they both correspond to the dihedron, and this is why the correct number of geometric crystal forms (in 3D) is 47 and not 48. If you introduce the difference between dome and sphenoid, this means you go beyond the geometric eigensymmetry and consider the physical properties of the faces. But then you have to do the same for all forms, not just the dihedron. And this leads to 130 crystal forms, that I have called crystallographic face forms (of these, 97 are affine face forms and 33 enantiomorphic pairs).
I have tried to explain this more than 10 years ago, but I see that the message did not go through. I take therefore the liberty of posting a link to the article where I have discussed this topic.
https://journals.iucr.org/j/issues/2015/04/00/gj5135/index.html
Massimo Nespolo
Université de Lorraine, Nancy (France)
Date: Wed, 4 Feb 2026 21:41:20 +0000
From: "Hummer, Daniel R" daniel.hummer@siu.edu
Subject: [MSA-talk] Re: dome vs. sphenoid
To: Kent Ratajeski kent.ratajeski@calvin.edu,
"msa-talk@minlists.org" msa-talk@minlists.org
Message-ID: <MN2PR07MB8045203DAE91582A114D3B87E098A@MN2PR07MB8045.nam
prd07.prod.outlook.com>
Content-Type: multipart/related; boundary="004_MN2PR07MB804520
3DAE91582A114D3B87E098AMN2PR07MB8045namp";
type="multipart/alternative"
Hi Kent,
This is actually a pretty interesting question. As best I can tell, this
question would ONLY be relevant for point group 2mm, because any point group of
less symmetry would have only one symmetry element generating the form, and any
point group of more symmetry would produce a form with more than two faces.
You’re correct that you can’t rely on the rules that you give in your message,
because in the case of a 2-fold axis and an intersecting mirror plane, the
“2-fold rotoinversion axis” (equivalent to the mirror plane) is actually
situated perpendicular to the 2-fold axis. So rules that prioritize various
symmetries along the SAME axis would not be relevant here. Since there are two
different symmetry elements (oriented differently) that happen to produce the
same form, my own personal answer would be that you could rightfully call it
either a dome or a sphenoid. In the Perkins et al. textbook, their chart of
forms lists point group 2mm has having a dome but NOT a sphenoid, but the
reason for not check marking the sphenoid is not clear to me:
https://geo.libretexts.org/Bookshelves/Geology/Mineralogy_%28Perkins_et_al.%29/10%3A_Crystal_Morphology_and_Symmetry/10.05%3A_Point_Groups_and_Crystal_Systems/10.5.01%3A_Forms_and_Point_Groups
Best,
Dan
DANIEL HUMMER
Associate Professor of Geology
SCHOOL OF EARTH SYSTEMS AND SUSTAINABILITY
MAIL CODE 4324
SOUTHERN ILLINOIS UNIVERSITY
PARKINSON LABORATORY 207
CARBONDALE, ILLINOIS 62901
daniel.hummer@siu.edumailto:daniel.hummer@siu.edu
P: 618.453.7386
SIU.EDU
[https://oit.siu.edu/enterprisesystems/email-sig-gen/images/Email-Logo-2023-maroon.png]
From: Kent Ratajeski via MSA-talk msa-talk@minlists.org
Sent: Monday, February 2, 2026 1:23 PM
To: msa-talk@minlists.org
Subject: [MSA-talk] dome vs. sphenoid
[EXTERNAL EMAIL ALERT]: Verify sender before opening links or attachments.
All,
This should be a quick one, as I must be missing something obvious. The usual
definitions of the "dome" and "sphenoid" crystal forms say something like
this...
-
A dome has two crystal faces that can be related to each other by a mirror
plane -
A sphenoid has two crystal faces that can be related to each by a two-fold
rotational axis.
Although my search was not comprehensive, none of the definitions I have seen
deal with the case where the two faces can be related to each other by BOTH a
mirror and a two-fold axis (as in the attached graphic). In that case, what
form is it: a dome or a sphenoid?
There are other rules of preferring one symmetry element over another one in the
accounting if both are present in the same crystal, e.g.,
* if a single axis produces more than one type of rotational symmetry (like a
2-fold and a 4-fold; i.e., different n’s), only count the higher n-fold
rotation
* if an axis produces both rotational and rotoinversional symmetry…
* if the n’s are the same, only count the rotational axis
* if the n’s are different, only count the higher n-fold operation
...but in this case, I can't figure out how to compare the different symmetry
operations (m vs. 2-fold), so these rules don't seem to apply.
Kent Ratajeski
Dr. Kent Ratajeski
Lecturer and Dice Mineralogical Museum Director
North Hall 081
Department of Geology, Geography, and Environment
Calvin University
3201 Burton St. SE
Grand Rapids, MI 49546
(616) 526-6769
https://calvin.edu/directory/people/kent-ratajeski
https://calvin.edu/dice