Editing Cuboctahedron (section)

== Construction ==
The cuboctahedron can be constructed in many ways:
* Its construction can be started by attaching two regular [[triangular cupola]]s base-to-base. This is similar to one of the Johnson solids, [[triangular orthobicupola]]. The difference is that the triangular orthobicupola is constructed with one of the cupolas twisted so that similar polygonal faces are adjacent, whereas the cuboctahedron is not. As a result, the cuboctahedron may also called the ''triangular gyrobicupola''.<ref>{{multiref
|{{harvnb|Berman|1971}}
|{{harvnb|Ogievetsky|Shlosman|2021|p=[https://books.google.com/books?id=UsspEAAAQBAJ&pg=PA477 477]}}
}}</ref>
* Its construction can be started from a [[Cube (geometry)|cube]] or a [[regular octahedron]], marking the midpoints of their edges, and cutting off all the vertices at those points. This process is known as [[Rectification (geometry)|rectification]], making the cuboctahedron being named the ''rectified cube'' and ''rectified octahedron''.{{sfn|van Leeuwen|Freixa|Cano|2023|p=[https://books.google.com/books?id=8S3nEAAAQBAJ&pg=PA50 50]}}
* An alternative construction is by cutting off all vertices ([[Truncation (geometry)|truncation]]) of a [[regular tetrahedron]] and beveling the edges. This process is termed [[Cantellation (geometry)|cantellation]], lending the cuboctahedron an alternate name of ''cantellated tetrahedron''.{{sfn|Linti|2013|p=[https://books.google.com/books?id=_4C7oid1kQQC&pg=RA7-PA41 41]}}
From all of these constructions, the cuboctahedron has 14 faces: 8 equilateral triangles and 6 squares. It also has 24 edges and 12 vertices.{{sfn|Berman|1971}}

The [[Cartesian coordinates]] for the vertices of a cuboctahedron with edge length <math>\sqrt{2}</math> centered at the origin are:{{sfn|Coxeter|1973|p=52|loc=§3.7 Coordinates for the vertices of the regular and quasi-regular solids}}
<math display="block"> (\pm 1, \pm 1, 0), \qquad (\pm 1, 0, \pm 1), \qquad (0, \pm 1, \pm 1). </math>