The great rhombicuboctahedron (Cundy and Rowlett 1989, p. 106) is the 26-faced Archimedean solid consisting of faces . It is sometimes called the rhombitruncated
cuboctahedron (Wenninger 1971, p. 29) or (improperly) the truncated cuboctahedron
(Ball and Coxeter 1987, p. 143; Cundy and Rowlett 1989, p. 106; Maeder
1997; Conway et al. 1999). It is illustrated above together with a wireframe
version and a net that can be used for its construction.

It is also the uniform polyhedron with Maeder index 11 (Maeder 1997), Wenninger index 15 (Wenninger 1989), Coxeter index 23 (Coxeter
et al. 1954), and Har'El index 16 (Har'El 1993). It has Schläfli
symbol t
and Wythoff symbol .

Some symmetric projections of the great rhombicuboctahedron are illustrated above.

The great rhombicuboctahedron is implemented in the Wolfram Language as UniformPolyhedron["GreatRhombicuboctahedron"].
Precomputed properties are available as PolyhedronData["GreatRhombicuboctahedron",
prop].

Confusingly, the term "great rhombicuboctahedron" is also used by various authors (e.g., Maeder 1997) to refer to the distinct unform
polyhedron with Maeder index 17 and Wenninger index 85. For reasons of clarity,
that solid is better referred to using Wenninger's term quasirhombicuboctahedron
(Wenninger 1971, p. 132).

The great rhombicuboctahedron is an equilateral zonohedron and the Minkowski sum of three cubes. It has Dehn
invariant 0 (Conway et al. 1999) but is not a space-filling
polyhedron. However, it can be combined with cubes and truncated octahedra into
a regular space-filling pattern.

Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, p. 138, 1987.Conway,
J. H.; Radin, C.; and Sadun, L. "On Angles Whose Squared Trigonometric
Functions Are Rational." Discr. Computat. Geom.22, 321-332, 1999.Coxeter,
H. S. M.; Longuet-Higgins, M. S.; and Miller, J. C. P. "Uniform
Polyhedra." Phil. Trans. Roy. Soc. London Ser. A246, 401-450,
1954.Cundy, H. and Rollett, A. "Great Rhombicuboctahedron or Truncated
Cuboctahedron. ." §3.7.6 in Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 106, 1989.Geometry
Technologies. "Rhombitruncated Cubeoctahedron." http://www.scienceu.com/geometry/facts/solids/rh_tr_cubeocta.html.Har'El,
Z. "Uniform Solution for Uniform Polyhedra." Geometriae Dedicata47,
57-110, 1993.Kasahara, K. "Two New Semiregular Polyhedrons."
Origami
Omnibus: Paper-Folding for Everyone. Tokyo: Japan Publications, p. 227,
1988.Maeder, R. E. "11: Truncated Cuboctahedron." 1997.
https://www.mathconsult.ch/static/unipoly/11.html.Wenninger,
M. J. "The Rhombitruncated Cuboctahedron." Model 15 in Polyhedron
Models. Cambridge, England: Cambridge University Press, p. 29, 1989.