The 26-faced
Archimedean solid
consisting of faces
. It is sometimes (improperly) called the truncated
cuboctahedron (Ball and Coxeter 1987, p. 143), and is also more properly called
the rhombitruncated cuboctahedron. It is uniform
polyhedron
and Wenninger model
. It has Schläfli
symbol t
and Wythoff symbol
.
The great rhombicuboctahedron is an equilateral zonohedron and the Minkowski sum of three cubes. 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.
Its dual is the disdyakis dodecahedron, also called the hexakis octahedron. The inradius
of the dual, midradius
of the solid and dual, and circumradius
of the solid for
are
(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
(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
(12)
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(13)
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The surface area and volume are
(14)
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(15)
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