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The augmented dodecahedron is Johnson solid 
, which is formed from augmentation
of one of the faces of the regular dodecahedron
by an equilateral pentagonal
pyramid. It consists of five equilateral
triangles and 11 regular pentagons. The solid
and net are illustrated above.
It is implemented in Wolfram Language as PolyhedronData["AugmentedDodecahedron"]
or PolyhedronData[
"Johnson", 58
].
