Great disrhombidodecahedron

{{Infobox polytope The great disrhombidodecahedron, giddird, or compound of twelve pentagrammic prisms is a uniform polyhedron compound. It consists of 60 squares and 24 pentagrams, with two pentagrams and four squares joining at a vertex.
 * image = UC37-12 pentagrammic prisms.png
 * type=Uniform
 * dim = 3
 * obsa = Giddird
 * comps=12 pentagrammic prisms
 * faces = 60 squares, 24 pentagrams
 * edges = 60+120
 * vertices = 60
 * verf = Compound of two isosceles triangles, edge lengths ($\sqrt{5}$–1)/2, $\sqrt{2}$, $\sqrt{2}$
 * army=Srid
 * reg=Giddird
 * symmetry = H3, order 120
 * circum = $$\sqrt{\frac{15-2\sqrt5}{20}} ≈ 0.72553$$
 * volume = $$3\sqrt{25-10\sqrt5}} ≈ 4.87380$$
 * density = 24
 * dih = 4–5/2: 90°
 * dih2 = 4–4: 36°
 * dual=Compound of twelve pentagrammic tegums
 * conjugate=Disrhombidodecahedron
 * conv = No
 * orientable=Yes
 * nat=Tame}}

It can be formed by combining the two chiral forms of the great chirorhombidodecahedron, which results in vertices pairing up and two components joining per vertex.

Its quotient prismatic equivalent is the pentagrammic prismatic dodecadakoorthowedge, which is fourteen-dimensional.

Vertex coordinates
The vertices of a great disrhombidodecahedron of edge length 1 are given by all permutations of: Plus all even permutations of:
 * $$\left(±\sqrt{\frac{5+2\sqrt5}{20}},\,±\sqrt{\frac{5-2\sqrt5}{20}},\,±\sqrt{\frac{5-2\sqrt5}{20}}\right),$$
 * $$\left(0,\,±\sqrt{\frac{5+\sqrt5}{40}},\,±\sqrt{\frac{5-\sqrt5}{8}}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{40}},\,±\sqrt{\frac{5-\sqrt5}{40}},\,±\sqrt{\frac{5-\sqrt5}{10}}\right).$$