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The following references may be useful when improving this article in the future: * Viana, Vera; Xavier, João Pedro; Aires, Ana Paula; Campos, Helena (2019). "Interactive Expansion of Achiral Polyhedra". In Cocchiarella, Luigi (ed.). ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics: 40th Anniversary - Milan, Italy, August 3-7, 2018. p. 1121. doi:10.1007/978-3-319-95588-9. ISBN 978-3-319-95588-9.

The truncated octahedron is the only tridimensional primitive parallelohedra.

(I'll correct that to –hedron.) Does tridimensional here mean 'in 3space' or something else? What does primitive mean? —Tamfang (talk) 05:56, 21 January 2011 (UTC)[reply]

Definitely means 3-space. I found primary parallelohedron [1]. Tom Ruen (talk) 18:19, 21 January 2011 (UTC)[reply]

may I suggest to use dotted lines for the invisible edges in the drawings of the projections? not using them leads to puzzling effects: so e.g. in the column "edge 4-6" ot the table of "orthogonal projections" you think to see pentagons as surface-polygons (in the first row...) thanx! --HilmarHansWerner (talk) 06:18, 2 January 2017 (UTC)[reply]

compared to similar articles (eg Octahedron) there is some missing basic information about dimensions...

where side length = a

Circumsphere (vertex) radius = 0.5 * sqrt(10) * a ~= 1.5811a

Midsphere (mid-edge) radius = 1.5 * a == 1.5a

Insphere(1) (square face) radius = sqrt(2) * a ~= 1.4142a

Insphere(2) (hexagonal face) radius = 0.5 * sqrt(6) * a ~= 1.2247a

Volume = (1/3) * sqrt(2) * (3a)^3 - sqrt(2) * a^3

also it only requires 6 (not 12) rectangles, of sides [a, 3a] with the short edges along where octagons meet, passing through the center, each corner mapping a vertex.

I'd edit them in, but templates and formatting aren't my forte, so any help is appreciated
74.214.226.120 (talk) 17:39, 19 January 2017 (UTC)[reply]

The last sentence of the section As a space-filling polyhedron is this:

"It has the symmetric group.'

This sentence has no meaning, for two reasons: 1) It is entirely unclear what the word "It" refers to, and 2) it is entirely unclear what the word "has" means here.

I hope someone knowledgeable about this topic can fix this problem.

I think that sentence was intended to describe the symmetries of the truncated octahedron, which are better described in section "As an Archimedean solid". It [the truncated octahedron] has [as its group of orientation-preserving symmetries] the symmetric group . But because the symmetries are better described elsewhere, I replaced this sentence with material about the truncated octahedron being the Cayley graph of , a different property. —David Eppstein (talk) 22:57, 21 January 2025 (UTC)[reply]

The photograph of the ancient Chinese die looks more like what you get if you truncate the points of an octahedron all the way down to the inscribed circle. You get irregular hexagon faces. Compare the photo with one I made in OpenSCAD:

• 
  Ancient Chinese die
• 
  Octahedron truncated to sphere

I actually always assumed that the regular truncated octahedron touched the sphere on every face, but this isn't the case. This is what you get if you force the width between opposite sides to be constant for all sides. This fact might deserve a mention in the article. ~Anachronist (talk) 04:27, 4 March 2025 (UTC)[reply]

It has the same combinatorial structure as the Archimedean truncated octahedron. To say more we would need a source that says more. —David Eppstein (talk) 05:42, 4 March 2025 (UTC)[reply]