Small ditrigonary icosidodecahedral antiprism

{{Infobox polytope The small ditrigonary icosidodecahedral antiprism or sidtidap, is a prismatic uniform polychoron that consists of 2 small ditrigonary icosidodecahedra, 12 pentagrammic antiprisms, and 40 tetrahedra. Each vertex joins 1 small ditrigonary icosidodecahedron, 3 pentagrammic antiprisms, and 4 tetrahedra.
 * type=Uniform
 * dim = 4
 * obsa = Sidtidap
 * cells = 40 tetrahedra, 12 pentagrammic antiprisms, 2 small ditrigonary icosidodecahedra
 * faces = 40+120 triangles, 24 pentagrams
 * edges = 60+120
 * vertices = 40
 * verf = Triangular cupola, edge lengths ($\sqrt{5‘‘–1)/2 (3 base edges), 1 (remaining edges)
 * coxeter = β2β5o3o
 * symmetry = H3×A1, order 240
 * army=Semi-uniform Dope
 * reg=Sidtidap
 * circum=√(5+√5)/8 ≈
 * height = √(√5–1)/2 ≈ 0.78615
 * hypervolume = √110+85√5/8 ≈ 2.16530
 * dich= Tet–3–stap: acos(–√(5+3√5)/20) ≈ 139.91776º
 * dich2= Sidtid–3–tet: acos(–√7–3√5/2) ≈ 105.66967º
 * dich3= Sidtid–5/2–stap: 90º
 * dual = Small triambic icosahedral antitegum
 * conv = No
 * orientable=Yes
 * nat=Tame}$