<p>Now all of the 230 space groups are realized by a natural occurring mineral.
I found this blog: <a href="https://crystalsymmetry.wordpress.com/230-2/" rel="nofollow noreferrer">crystalsymmetry.wordpress.com</a> where space groups are listed with at least one chemical compound is listed for each space group. Minerals are listed for all of the space groups.</p>
<p>For example, Benitoite has fairly unusual crystal symmetry. I think it was first mineral found for P-6c2 space group.</p>
<h1>188 P-6c2 Example – Benitoite, BaTi(Si3O9)</h1>
<p>From <a href="http://rruff.info/uploads/ZK74_139.pdf" rel="nofollow noreferrer">Crystal Structure of Benitoite.</a></p>
<p>From a crystallographical point of view this compound (Benitoite)
is especially interesting, being the only known member of the ditrigonalbipyramidal
symmetry class.</p>

CC BY-SA 3.0
2017-07-24T10:51:43.057Z
"Not all..." It looks like the blog/poster claims all 230, or am I misunderstanding the intent of the poster? Is there at least proof-of-incompleteness space group that has no known mineral?
uhoh
CC BY-SA 3.0
2017-07-20T13:12:59.697Z
2017-09-22T12:05:40.793Z
2020-06-18T08:25:19.090Z
Earth Science Expatriate
<p>Quoting a mineralogist friend of mine:</p>

<blockquote>
  <p>I <em>think</em> there are mineral representatives of all 230 known by now - some of the groups are much rarer than others, but there is nothing specifically prohibiting...</p>
</blockquote>

<p>This shouldn't be too hard to figure out. There are databases that contain this information, webmineral is one of them. Here an example mineral called <a href="http://webmineral.com/data/Lewisite.shtml" rel="nofollow noreferrer">lewisite</a> where you can see: Space Group: F d3m . Unfortunately, that website does not aggregate space group data. Maybe it's possible to contact the people who run the website to see if it's possible to add this feature.</p>

CC BY-SA 3.0
2017-07-22T06:36:35.690Z
2017-07-22T06:36:35.690Z
Gimelist
<p>Well, one way would be to look through <a href="https://www.amazon.co.uk/Introduction-Rock-Forming-Minerals-W-Deer/dp/0903056275" rel="nofollow noreferrer">The rock forming minerals</a> and see how many are represented.  I strongly suspect that not all would be, so from that perspective the answer would be No. </p>

<p>But from an inspection perspective..  For any given mineral structure, we can make changes by simply substituting various cations and anions as in <a href="https://en.wikipedia.org/wiki/Pyroxene" rel="nofollow noreferrer">pyroxene</a>; for example, we can substitute Mg(2+) for Fe(2+). Or SiO4(4-) for AlO4(5-) - requiring other changes. So, assuming you had suitable equipment, you could find a naturally occurring crystal that was close to the desired symmetry group and tweak it with substitutions until it matched that group.  Or more simply, adjust the pressure and temperature until the symmetry changed. There is a lot of phase space to explore.</p>

<p>So from that perspective, the answer would be probably yes, we just haven't synthesized them all yet.</p>

CC BY-SA 3.0
2017-07-22T06:34:30.780Z
The rock forming minerals are only a small section of all 4000-something minerals described. Limiting your search to only those would miss quite a lot. Also, taking known minerals (like pyroxenes) and "tweaking" in pressure-temperature-composition space is a really labour-intensive and inefficient way of trying to make new minerals with other space groups. I know - this is what I do for a living at the moment.
Gimelist
CC BY-SA 3.0
2017-07-20T12:18:19.813Z
2017-07-20T12:18:19.813Z
Andrew Jon Dodds
<p>Every mineral has it's own internal building scheme, a lattice on which it's atoms lie. Mathematically, this can be described by the <a href="https://en.wikipedia.org/wiki/Space_group" rel="noreferrer">space group</a> of the mineral. From mathematical considerations it's known that there are exactly 230 symmetry groups which can occur as the space group of a mineral. Now my question is: Is each of the 230 space groups realized as the symmetry group of a mineral?</p>

CC BY-SA 3.0
2017-07-20T08:29:29.143Z
My guess is probably not but I don't have any hard evidence.
bon
CC BY-SA 3.0
2017-10-17T11:11:55.317Z
A similar question on physics.SE: https://physics.stackexchange.com/questions/127716/how-many-of-the-230-crystallographic-groups-are-realized-in-nature
marcin
<crystallography>
Is every space group realized by some mineral?
agb
# Is every space group realized by some mineral?

(Asked by: username_0 on 2017-07-19)

Every mineral has it's own internal building scheme, a lattice on which it's atoms lie. Mathematically, this can be described by the [space group](https://en.wikipedia.org/wiki/Space_group) of the mineral. From mathematical considerations it's known that there are exactly 230 symmetry groups which can occur as the space group of a mineral. Now my question is: Is each of the 230 space groups realized as the symmetry group of a mineral?

**Tags:** crystallography

> **Comments:**
> **username_1**: My guess is probably not but I don't have any hard evidence.  
> **username_2**: A similar question on physics.SE: https://physics.stackexchange.com/questions/127716/how-many-of-the-230-crystallographic-groups-are-realized-in-nature  

---

## 3 answers

### Answer by username_3 on 2017-07-20. Score: 5

Now all of the 230 space groups are realized by a natural occurring mineral.
I found this blog: [crystalsymmetry.wordpress.com](https://crystalsymmetry.wordpress.com/230-2/) where space groups are listed with at least one chemical compound is listed for each space group. Minerals are listed for all of the space groups.

For example, Benitoite has fairly unusual crystal symmetry. I think it was first mineral found for P-6c2 space group.

# 188 P-6c2 Example – Benitoite, BaTi(Si3O9)

From [Crystal Structure of Benitoite.](http://rruff.info/uploads/ZK74_139.pdf)

From a crystallographical point of view this compound (Benitoite)
is especially interesting, being the only known member of the ditrigonalbipyramidal
symmetry class.

> **Comments:**
> **username_4**: "Not all..." It looks like the blog/poster claims all 230, or am I misunderstanding the intent of the poster? Is there at least proof-of-incompleteness space group that has no known mineral?  

---

### Answer by username_5 on 2017-07-22. Score: 1

Quoting a mineralogist friend of mine:

> I *think* there are mineral representatives of all 230 known by now - some of the groups are much rarer than others, but there is nothing specifically prohibiting...

This shouldn't be too hard to figure out. There are databases that contain this information, webmineral is one of them. Here an example mineral called [lewisite](http://webmineral.com/data/Lewisite.shtml) where you can see: Space Group: F d3m . Unfortunately, that website does not aggregate space group data. Maybe it's possible to contact the people who run the website to see if it's possible to add this feature.


---

### Answer by username_6 on 2017-07-20. Score: 0

Well, one way would be to look through [The rock forming minerals](https://www.amazon.co.uk/Introduction-Rock-Forming-Minerals-W-Deer/dp/0903056275) and see how many are represented. I strongly suspect that not all would be, so from that perspective the answer would be No.

But from an inspection perspective.. For any given mineral structure, we can make changes by simply substituting various cations and anions as in [pyroxene](https://en.wikipedia.org/wiki/Pyroxene); for example, we can substitute Mg(2+) for Fe(2+). Or SiO4(4-) for AlO4(5-) - requiring other changes. So, assuming you had suitable equipment, you could find a naturally occurring crystal that was close to the desired symmetry group and tweak it with substitutions until it matched that group. Or more simply, adjust the pressure and temperature until the symmetry changed. There is a lot of phase space to explore.

So from that perspective, the answer would be probably yes, we just haven't synthesized them all yet.

> **Comments:**
> **username_5**: The rock forming minerals are only a small section of all 4000-something minerals described. Limiting your search to only those would miss quite a lot. Also, taking known minerals (like pyroxenes) and "tweaking" in pressure-temperature-composition space is a really labour-intensive and inefficient way of trying to make new minerals with other space groups. I know - this is what I do for a living at the moment.  

---

