The Triaugmented Truncated Dodecahedron is the Johnson solid ,and it can be constructed by means of the Metabiaugmented Truncated Dodecahedron ,if we have the Metabiaugmented Truncated Dodecahedron we only need to add another pentagonal cupola on a decagonal face of the Metabiaugmented Truncated Dodecahedron such that the third pentagonal cupola and the second pentagonal cupola are not adjacent.

　

 

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Reference   http://www.mathworld.wolfram.com