Editing Cuboctahedron (section)

== Related polyhedra and honeycomb ==
{{multiple image
 | image1 = cuboctahedron.png
 | image2 = cubohemioctahedron.png
 | image3 = octahemioctahedron.png
 | footer = The cuboctahedron, [[cubohemioctahedron]], and [[octahemioctahedron]].
 | total_width = 400
}}
The cuboctahedron shares its [[Skeleton (topology)|skeleton]] with the two [[nonconvex uniform polyhedron|nonconvex uniform polyhedra]], the [[cubohemioctahedron]] and [[octahemioctahedron]]. These polyhedrons are constructed from the skeleton of a cuboctahedron in which the four hexagonal planes bisect its diagonal, intersecting its interior. Adding six squares or eight equilateral triangles results in the cubohemicotahedron or octahemioctahedron, respectively.<ref>{{multiref
|{{harvnb|Pisanski|Servatius|2013|p=[https://books.google.com/books?id=3vnEcMCx0HkC&pg=PA108 108]}}
|{{harvnb|Barnes|2012|p=[https://books.google.com/books?id=BQhEAAAAQBAJ&pg=PA53 53]}}
}}</ref>

The cuboctahedron [[covering space|2-covers]] the [[tetrahemihexahedron]], which accordingly has the same [[abstract polytope|abstract]] [[vertex figure]] (two triangles and two squares: <math> 3 \cdot 4 \cdot 3 \cdot 4 </math>) and half the vertices, edges, and faces. (The actual vertex figure of the tetrahemihexahedron is <math display="inline"> 3 \cdot 4 \cdot \frac{3}{2} \cdot 4 </math>, with the <math display="inline"> \frac{a}{2} </math> factor due to the cross.){{sfn|Grünbaum|2003|p=[https://books.google.com/books?id=WoaxgpHu19gC&pg=PA338 338]}}

[[File:TetraOctaHoneycomb-VertexConfig.svg|160px|thumb|The dissection into square pyramids and tetrahedrons]]
The cuboctahedron can be dissected into 6 [[square pyramid]]s 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]].{{sfn|Posamentier|Thaller|Dorner|Geretschläger|2022|p=[https://books.google.com/books?id=DGxYEAAAQBAJ&pg=PA234 233&ndash;235]}}