# What is the name of this geometric figure? **URL:** \ **Category:** Factual Questions\ **Created:** [June 24, 2008, 3:33am UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011 "2008-06-24T03:33:53Z")\ **Posts on this page:** 19\ **Page:** 1
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [June 24, 2008, 3:33am UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/1 "2008-06-24T03:33:53Z")
Link to the least-lousy picture I could find of an example: [http://www.steelpillow.com/polyhedra/icosa/tidystelfacet/sphere\_cells.png](http://www.steelpillow.com/polyhedra/icosa/tidystelfacet/sphere_cells.png) Only with each two parallel bands in the example replaced by single line. It’s related to the icosahedron obviously and it’s symmetrical, but it’s not a semi-regular polyhedron since neither the triangles nor the hexagons are regular. I _think_ it’s what you get when you take a truncated icosahedron (soccerball pattern) and then truncate it again. It may not be obvious from the picture, but it’s edges form ten great circles each dividing a sphere in half, and so it could be considered a family with the octahedron, cuboctahedron, and icosidodecahedron, which do the same thing with three, four, and six great circles. In fact they could be considered corresponding to the four Platonic solids that have three, four, six and ten opposing vertices and faces. Anyway, as this long-winded explanation shows, it would really help if I could knew this beast’s name. ---
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [June 24, 2008, 3:29pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/2 "2008-06-24T15:29:19Z")
A dodecahedron? [![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/375px-Dodecahedron.svg.png) ](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/375px-Dodecahedron.svg.png) ---
**Author:** ![Vorpal\_Blade](https://avatars.discourse-cdn.com/v4/letter/v/9de0a6/32.png) [@Vorpal\_Blade](https://boards.straightdope.com/u/Vorpal_Blade)\ **Post date:** [June 24, 2008, 4:18pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/3 "2008-06-24T16:18:27Z")
[QUOTE=Lumpy] … if I could knew this beast’s name. [/QUOTE] Ball of yarn? ---
**Author:** ![Dead\_Badger](https://avatars.discourse-cdn.com/v4/letter/d/848f3c/32.png) [@Dead\_Badger](https://boards.straightdope.com/u/Dead_Badger)\ **Post date:** [June 24, 2008, 5:10pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/4 "2008-06-24T17:10:59Z")
It’s a tricky one; I agree that it might be a twice-truncated icosahedron, but I’m having a little trouble visualising it from the picture provided. Afraid I’ve got to run off so can’t chase this down more, but there’s a rather magnificent [Encyclopedia Polyhedra](http://www.georgehart.com/virtual-polyhedra/vp.html) that might be of use to you; it has a whole bunch of VRML 3D models to view if you’ve got the right browser plugin. Hope this helps… ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 24, 2008, 5:29pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/5 "2008-06-24T17:29:13Z")
> [@](#): > > I think it’s what you get when you take a truncated icosahedron (soccerball pattern) and then truncate it again. This appears to be correct. I don’t know if there’s a standard name for that, though. ---
**Author:** ![1010011010](https://avatars.discourse-cdn.com/v4/letter/1/ea666f/32.png) [@1010011010](https://boards.straightdope.com/u/1010011010)\ **Post date:** [June 24, 2008, 5:35pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/6 "2008-06-24T17:35:43Z")
“Truncated truncated icosahedron” seems to be the most common term I’ve seen while meandering around some geometric origami and math websites. ---
**Author:** ![1010011010](https://avatars.discourse-cdn.com/v4/letter/1/ea666f/32.png) [@1010011010](https://boards.straightdope.com/u/1010011010)\ **Post date:** [June 24, 2008, 6:09pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/7 "2008-06-24T18:09:13Z")
… ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [June 24, 2008, 6:37pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/8 "2008-06-24T18:37:55Z")
Searching that site found the image used near the bottom of this page. The caption there is “Sphere intersecting the infinite cells of the stellated icosahedron”. [http://www.steelpillow.com/polyhedra/icosa/tidystelfacet/TidyStelFacet.htm](http://www.steelpillow.com/polyhedra/icosa/tidystelfacet/TidyStelFacet.htm) ---
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [June 24, 2008, 8:18pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/9 "2008-06-24T20:18:54Z")
[QUOTE=Enola Straight] A dodecahedron? [http://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/375px-Dodecahedron.svg.png](http://upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Dodecahedron.svg/375px-Dodecahedron.svg.png) [/QUOTE] On second thought… > **[Truncated icosahedron](https://en.wikipedia.org/wiki/Truncated_icosahedron)** > > In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. Intuitively, it may be regarded as footballs (or soccer balls) that are typically patterned with white hexagons and black pentagons. Geodesic dome structures, such as those whose architecture Buckminster Fuller pioneered, are often based on this structure. It is an example of an Archimedean solid, as well as a Goldberg polyhedron. > The truncated icosahedron can... ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [June 24, 2008, 8:19pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/10 "2008-06-24T20:19:27Z")
[QUOTE=Dead Badger] It’s a tricky one; I agree that it might be a twice-truncated icosahedron, but I’m having a little trouble visualising it from the picture provided. Afraid I’ve got to run off so can’t chase this down more, but there’s a rather magnificent [Encyclopedia Polyhedra](http://www.georgehart.com/virtual-polyhedra/vp.html) that might be of use to you; it has a whole bunch of VRML 3D models to view if you’ve got the right browser plugin. Hope this helps… [/QUOTE] Wonderful site DB! The closest I found was quasi-regular polyhedra, which my figure doesn’t quite meet the technical defintion of, but shares the property of the edges forming great circles. It’s similar in appearance to the dodecadodecahedron, except it’s convex. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [June 17, 2012, 2:37pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/11 "2012-06-17T14:37:45Z")
reviving this thread because I have something new to add- a better picture of what I was trying to describe: [![Imgur](https://live.staticflickr.com/7017/6542727421_d8361a84e9_z.jpg "Spherical Dodecadodecahedron") ](https://www.flickr.com/photos/powerofankur/6542727421/) ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [June 18, 2012, 6:16am UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/12 "2012-06-18T06:16:10Z")
A [dodecadodecahedron.](http://en.wikipedia.org/wiki/Dodecadodecahedron) Here’s a list of all kinds of [uniform polyhedra,](http://en.wikipedia.org/wiki/List_of_uniform_polyhedra) too. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [February 10, 2014, 1:36pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/13 "2014-02-10T13:36:03Z")
Image search for [Triaxial Sphere](http://www.bing.com/images/search?q=triaxial+sphere&go=&qs=n&form=QBIR&pq=triaxial+sphere&sc=0-9&sp=-1&sk=) leads to several examples of what I was talking about. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [February 12, 2014, 1:40am UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/14 "2014-02-12T01:40:51Z")
Irregular pentagon. irregular is perhaps due to error in the lines - it could be a regular pentagon if the lines that formed the sides were accurate. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 12, 2014, 2:08am UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/15 "2014-02-12T02:08:55Z")
A pentagon is a two-dimensional figure. This is three-dimensional. ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [February 12, 2014, 5:03am UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/16 "2014-02-12T05:03:16Z")
According to the Balcones Forge newsletter from [April 2008 (warning: PDF)](https://sites.google.com/a/balconesforge.org/www/apr08.pdf?attredirects=0), it’s an Icosidodecahedron. We made one out of 5 strips of steel. There are some pictures if you care to download it. Rob ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [February 12, 2014, 1:16pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/17 "2014-02-12T13:16:17Z")
> [@sweeteviljesus](#): > > According to the Balcones Forge newsletter from [April 2008 (warning: PDF)](https://sites.google.com/a/balconesforge.org/www/apr08.pdf?attredirects=0), it’s an Icosidodecahedron. We made one out of 5 strips of steel. There are some pictures if you care to download it. > > Rob Close but no cigar. An Icosidodecahedron requires six bands; the figure this thread is about requires ten. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [February 12, 2014, 7:16pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/18 "2014-02-12T19:16:23Z")
In France they call it a [boule](http://www.petanquestock.com/Files/23385/Img/24/LA-BOULE-D-OR-TBK.jpg). 🙂 ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [February 12, 2014, 7:34pm UTC](https://boards.straightdope.com/t/what-is-the-name-of-this-geometric-figure/454011/19 "2014-02-12T19:34:23Z")
> [@Colophon](#): > > In France they call it a [boule](http://www.petanquestock.com/Files/23385/Img/24/LA-BOULE-D-OR-TBK.jpg). 🙂 In Hogwarts they call that a snitch. But seriously, looking at the OP’s example, it looks like a **spherical dodecadodecahedron,** which legend holds can only be destroyed in the very fires that forged it.