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The elongated dodecahedron, also known as the extended rhombic dodecahedron and rhombo-hexagonal dodecahedron, is a space-filling polyhedron
and primary parallelohedron bounded by
eight rhombi of angle (at the poles) and an equatorial
zone of four equilateral hexagons having opposite
angles of
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with the remaining four angles equal (Coxeter 1973, pp. 29-30 and 257).
The elongated dodecahedron can be constructed by stretching a rhombic dodecahedron until the middle ring of rhombi become regular hexagons. Note that in this case, the term "elongated" refers to stretching of some of the existing faces as opposed to insertion of additional faces, the latter meaning of which is used in the naming of Johnson solids.
It is implemented in the Wolfram Language as PolyhedronData["ElongatedDodecahedron"].
The elongated dodecahedron has surface area and volume given by
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(1)
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(2)
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and moment of inertia tensor
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(3)
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for a uniform solid with mass .