Triangular antiditetragoltriate

{{Infobox polytope The triangular antiditetragoltriate or traddet is a convex isogonal polychoron and the first member of the antiditetragoltriate family. It consists of 6 triangular prisms, 18 rectangular pyramids, and 18 tetragonal disphenoids of two kinds. 2 triangular prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.
 * type=Isogonal
 * dim = 4
 * img= auto
 * off=auto
 * cells = 9+9 tetragonal disphenoids, 18 rectangular pyramids, 6 triangular prisms
 * faces = 6 triangles, 36+36 isosceles triangles, 18 rectangles
 * edges = 18+18+36
 * vertices = 18
 * verf = Biaugmented triangular prism
 * symmetry = A2≀S2, order 72
 * obsa = Traddet
 * army=Traddet
 * reg=Traddet
 * custom_measure = (based on same duoprisms as optimized triangular ditetragoltriate)
 * 3l = Edges of smaller triangle (18): 1
 * el2 = Lacing edges (36): $$\frac{\sqrt{\frac{5+\sqrt6}{3}} ≈ 1.57581$$
 * el3 = Edges of larger triangle (18): $$\frac{2+\sqrt6}{2} ≈ 2.22475$$
 * circum = $$\frac{6+\sqrt6}{6} ≈ 1.40825$$
 * dual=Triangular antitetrambitriate
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

It can be formed as the convex hull of 2 oppositely oriented semi-uniform triangular duoprisms where the larger triangles is more the twice the edge length of the smaller one.