The Metabiaugmented Truncated Dodecahedron is the Johnson solid ,which is similar to the Augmented Truncated Dodecahedron ,we can use the Augmented Truncated Dodecahedron first and we construct another pentagonal cupola on the  decagonal  face of the Augmented Truncated Dodecahedron such that the two pentagonal cupola are not parallel and not adjacent.

 

 

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