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.
The small cubicuboctahedron is a faceted version of the great rhombicuboctahedron.
The skeleton of the great rhombicuboctahedron is the great rhombicuboctahedral graph, illustrated above in a number of embeddings.
The dual polyhedron of the great rhombicuboctahedron is the disdyakis dodecahedron, both of
which are illustrated above together with their common midsphere.
The inradius 
of the dual, midradius 
of the solid and dual, and circumradius 
of the solid for 
are
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(1)
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(2)
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(3)
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(4)
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(5)
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(6)
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Additional quantities are
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(7)
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(8)
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(9)
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(10)
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(11)
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The distances between the solid center and centroids of the square and octagonal faces are
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(12)
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(13)
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The surface area and volume are
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(14)
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(15)
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." §3.7.6 in