Metabiaugmented truncated dodecahedron

The metabiaugmented truncated dodecahedron, or mabautid, is one of the 92 Johnson solids (J70). It consists of 2+2+2+2+2+4+4+4+4+4 triangles, 2+4+4 squares, 2 pentagons, and 2+2+2+4 decagons. It can be constructed by attaching two pentagonal cupolas to two non-opposite, non-adjacent decagonal faces of the truncated dodecahedron..

Vertex coordinates
A metabiaugmented truncated dodecahedron of edge length 1 has vertices given by all even permutations of: Plus the following additional vertices:
 * (0, ±1/2, ±(5+3$\sqrt{2}$)/4),
 * (±1/2, ±(3+$\sqrt{5}$)/4, ±(3+$\sqrt{2}$)/2),
 * (±(3+$\sqrt{2}$)/4, ±(1+$\sqrt{(5+√5)/2}$)/2, ±(2+$\sqrt{2+√2}$)/2),
 * (±(15+13$\sqrt{2+√2}$)/20, ±1/2, 3(5+$\sqrt{5}$)/10),
 * (±(25+13$\sqrt{(23+23√5)/30}$)/20, ±(1+$\sqrt{3}$)/4, (25+$\sqrt{15}$)/20),
 * (±(10+9$\sqrt{(65–2√5)/75}$)/10, 0, (15+$\sqrt{(5+√5)/10}$)/20),