Talk:Cuboctahedron

It would be fun to add a section Cuboctahedra in the arts, if anyone can remember which episode of Old Star Trek had the badguys zap some of the crew into the form of little plaster cubocs. --Anton Sherwood 01:33, 13 January 2006 (UTC)

It was By Any Other Name. Joule36e5 (talk) 22:18, 18 August 2008 (UTC)

Then there's the legendary Coriolis stations in Elite. olofito 01:17, 29 January 2006 (UTC)

I think "L¹ ball" means a regular cross-polytope. —Tamfang 06:42, 22 March 2006 (UTC)

Thanks, made the change (that sentence was my very first wikipedia contribution!). In other matters, it seems this section can use some cleaning up. The "Dymaxion" sentence, while interesting, doesn't seem to qualify as a geometric relation. There are statements about Johnson solids that are separated and should probably be together. Dshin

User:Ptah changed

${\displaystyle A=(6+2{\sqrt {3}})a^{2}\approx 9.46410162a^{2}}$

to

${\displaystyle A=(6+4{\sqrt {3}})a^{2}\approx 12.92820323a^{2}}$

Eight triangles of unit base and height √3/2 gives 8*√3/4 = 2√3, not 4√3. Have I missed something? —Tamfang (talk) 08:23, 22 January 2008 (UTC)

Here's comparison:

More information jpg, svg ...

jpg	svg	png

Close

Professor M. Fiendish 05:16, 23 August 2009 (UTC)

Pros and cons.

Pros of the jpg: shading, transparent faced

Cons: ugly background

Pros of SVG: infinite res, also transparent faces and bg

cons: no shading

pros of png: transparent bg

cons: no shading, faces arent transparent.

WE SHOULD USE THE SVG!

. 2603:7080:17F0:F40:C5B3:920A:CC87:7460 (talk) 14:53, 14 September 2024 (UTC)

User:KoenDelaere changed the vertex coordinates to

(±√2,0,0)

(0,±√2,0)

(±1/√2,±1/√2,±1)

User:Tomruen reverted to (±1,±1,0) and its permutations, which are preferred because they're more symmetric; but I'd like to mention for the record that KoenDelaere's version is not wrong – it's an eighth-rotation in (x,y). —Tamfang (talk) 01:57, 1 March 2010 (UTC)

The table at the top right of the article ought, I think, to give its Schläfli symbol as ${\displaystyle {\begin{Bmatrix}3\\4\end{Bmatrix}}}$ , by analogy with icosidodecahedron. I would change it, but I can't figure out how to get at the table for editing purposes. Maproom (talk) 12:32, 27 January 2011 (UTC)

There's different notations, see Uniform_polyhedron#Wythoff_construction_operators. They should be consistent in the tables, so I changed it. Tom Ruen (talk) 19:51, 27 January 2011 (UTC)

It's now ${\displaystyle {\begin{Bmatrix}4\\3\end{Bmatrix}}}$ with the tag {{dubious|reason=What is this notation? This is not on the form of a Schläfli symbol.}}. This is Coxeter's extension of a Schläfli symbol. Imagine the CD symbol's one ringed node at the middle left; the numbers represent its two edges. —Tamfang (talk) 22:02, 9 August 2024 (UTC)

Amazingly, the cuboctahedron (and a few other recognizable geometric shapes, but mostly cuboctahedra) is the shape taken by "COPII" proteins when they are transported from the "endoplasmic reticulum" to the "golgi apparatus" http://www.nature.com/nrm/journal/v7/n10/images/nrm2025-f2.jpg — Preceding unsigned comment added by 129.215.109.69 (talk) 12:58, 18 September 2015 (UTC)

The following Wikimedia Commons file used on this page has been nominated for deletion:

• Rhombicdodecahedron.jpg

Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 17:53, 18 May 2019 (UTC)

(This is the bad section) The cuboctahedron can be dissected into 6 square pyramids and 8 tetrahedra meeting at a central point. This dissection is expressed in the tetrahedral-octahedral honeycomb where pairs of square pyramids are combined into octahedra. Glenneric1 (talk) 13:10, 27 March 2023 (UTC)

It's a square dipyramid, dissected into cells of the lattice mentioned in the second sentence. A picture of a dissected CO would still be good. —Tamfang (talk) 05:51, 5 April 2023 (UTC)

In https://archive.org/details/intertwined_polysigned_p3_on_the_equator is possible to look an cuboctahedron compared to the hull made with triangles, similar to the icosidodecahedron

What is hamiltonian paths? That came out of nowhere.

By the way, how many Hamilton cycles are there? How many Euler cycles? —Tamfang (talk) 01:34, 4 October 2025 (UTC)

I think that was meant to say "has" instead of "is". I have edited accordingly. — LucasBrown 02:30, 4 October 2025 (UTC)

hm, I guess I ought to generate a list of Euler cycles. —Antonissimo (talk) 01:02, 7 April 2026 (UTC)

  Y Merge completed Klbrain (talk) 18:49, 16 July 2026 (UTC)

I changed the following, original:

Buckminster Fuller found that the cuboctahedron is the only polyhedron in which the distance between its center to the vertex is the same as the length of its edges. In other words, it has the same length vectors in three-dimensional space, known as vector equilibrium.

The claim attributed to Fuller is obviously false even if only convex polyhedra are considered, as the triangular cupola and triangular orthobicupola share this property. The citation was a dubious "sacred geometry" book that fails WP:FRINGE. I couldn't readily find a better citation, and Fuller's own writings are as incomprehensible to me. I replaced the citation with a "citation needed" and replaced the statement attributed to Fuller with a mathematically correct one, removing the "only." Not ideal but I would say it's an improvement.

I'm aware through osmosis that Fuller did describe the cuboctahedron as "vector equilibrium." I would argue that both the "circumradius = edge length" property and Fuller's fascination with it are notable enough for inclusion and good sources should be out there, but I'm not sure where to look. 11wx (talk) 20:50, 9 April 2026 (UTC)