Triaugmented truncated dodecahedron

The triaugmented truncated dodecahedron, or tautid, is one of the 92 Johnson solids (J71). It consists of 1+1+3+3+3+6+6+6+6 triangles, 3+6+6 squares, 3 pentagons, and 3+3+3 decagons. It can be constructed by attaching pentagonal cupolas to three mutally non-adjacent decagonal faces of the truncated dodecahedron..

Vertex coordinates
A triaugmented 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),
 * (±1/2, –3(5+$\sqrt{(5+2√5)/15}$)/10, –(15+13$\sqrt{5}$)/20),
 * (±(1+$\sqrt{5}$)/4, –(25+$\sqrt{5}$)/20, –ª25+13$\sqrt{5}$)/20),
 * (0, –(15+$\sqrt{5}$)/20, –(10+9$\sqrt{5}$)/10).