Editing Cuboctahedron (section)

=== Measurement and other metric properties ===
The surface area of a cuboctahedron <math> A </math> can be determined by summing all the area of its polygonal faces. The volume of a cuboctahedron <math> V </math> can be determined by slicing it off into two regular triangular cupolas, summing up their volume. Given that the edge length <math> a </math>, its surface area and volume are:{{sfn|Berman|1971}}
<math display="block"> \begin{align}
A &= \left(6+2\sqrt{3}\right)a^2 &&\approx 9.464a^2 \\
V &= \frac{5 \sqrt{2}}{3} a^3 &&\approx 2.357a^3.
\end{align}</math>

The dihedral angle of a cuboctahedron can be calculated with the angle of triangular cupolas. The dihedral angle of a triangular cupola between square-to-triangle is approximately 125°, that between square-to-hexagon is 54.7°, and that between triangle-to-hexagon is 70.5°. Therefore, the dihedral angle of a cuboctahedron between square-to-triangle, on the edge where the base of two triangular cupolas are attached is 54.7° + 70.5° approximately 125°. Therefore, the dihedral angle of a cuboctahedron between square-to-triangle is approximately 125°.{{sfn|Johnson|1966}}

[[File:A3-P5-P3.gif|thumb|The process of ''[[jitterbug transformation]]'']]
[[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 distance between its edges. In other words, it has the same length vectors in three-dimensional space, known as ''vector equilibrium''.{{sfn|Cockram|2020|p=[https://books.google.com/books?id=jrITEAAAQBAJ&pg=PA53 53]}} The rigid struts and the flexible vertices of a cuboctahedron may also be transformed progressively into a [[regular icosahedron]], regular octahedron, regular tetrahedron. Fuller named this the ''[[jitterbug transformation]]''.{{sfn|Verheyen|1989}}

A cuboctahedron has the [[Rupert property]], meaning there is a polyhedron of the same or larger size that can pass through its hole.{{sfn|Chai|Yuan|Zamfirescu|2018}}