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It looks a bit like an inflated rhombic dodecahedron—if one replaces each face of the rhombic dodecahedron with a single vertex and four triangles in a regular fashion one ends up with a disdyakis dodecahedron.
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The dihedral angle of 143° 7' 48" is wrong, if that means the angle between to faces: it is ≈ 155,08° (directly measured on a 3D-model in CATIA). See also the formula for "Flächenwinkel" in
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Thanks! I went to my source (Williams) and listed as 155° 4' 56". It looks like 143d7'48" was incorrectly used from the
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The cartesian coordinates given in the article can be simplified by noting that sqrt(27+18sqrt(2)) equals 3+3sqrt(2).
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It can be constructed by adding a low pyramid to each face of a rhombic dodecahedron
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