Bitetrahedral diacositetracontachoron

{{Infobox polytope The bitetrahedral diacositetracontachoron or bittid, also known as the octafold icosidodecaswirlchoron, is a convex isogonal polychoron that consists of 720 rhombic disphenoids and 1440 phyllic disphenoids. 12 rhombic and 24 phyllic disphenoids join at each vertex. However, it cannot be made uniform. It is the second in a series of isogonal icosidodecahedral swirlchora.
 * type=Isogonal
 * img=auto
 * off=auto
 * obsa = Bittid
 * dim = 4
 * cells = 720 rhombic disphenoids, 1440 phyllic disphenoids
 * faces = 1440 isosceles triangles, 2880 scalene triangles
 * edges = 480+480+1440
 * vertices = 240
 * verf = Chiral ditriakis tetrahedron
 * symmetry = H4+×2/5, order 2880
 * army=Bittid'
 * reg=Bittid
 * custom_measure = (based on 2 hexacosichora of edge length 1)
 * el = 12-valence lacing (480: $$\frac{\sqrt{12-7\sqrt2+4\sqrt5-3\sqrt{10}}{2} ≈ 0.62408$$
 * el2 = Edges of hexacosichora (1440): 1
 * el3 = 6-valence lacing (480: $$\frac{\sqrt{165-80\sqrt2+55\sqrt5-48\sqrt{10}}{4} ≈ 1.20045$$
 * circum = $$\frac{1+\sqrt5}{2} ≈ 1.61803$$
 * dual = Ditruncated-tetrahedral diacositetracontachoron
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

It can be formed as the convex hull of two hexacosichora, oriented such that the hull of 2 icositetrachoric sets of 24 vertices from each is a bitetracontoctachoron.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{54+6\sqrt{37+8\sqrt{10}}}}{6}$$ ≈ 1:1.67794.

Vertex coordinates
Vertex coordinates for a bitetrahedral diacositetracontachoron, created from the vertices of a hexacosichoron of edge length 1, are given by all permutations of: as well as all even permutations of: as well as all permutations and even sign changes of: as well as all permutations and odd sign changes of:
 * $$\left(0,\,0,\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt2+\sqrt{10}}{4},\,±\frac{\sqrt2+\sqrt{10}}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{2\sqrt2+\sqrt{10}}{4}\right),$$
 * $$\left(\frac{\sqrt{10}-\sqrt2}{8},\,\frac{3\sqrt2+\sqrt{10}}{8},\,\frac{3\sqrt2-\sqrt{10}}{8},\,\frac{3\sqrt2-\sqrt{10}}{4}\right),$$
 * $$\left(\frac{\sqrt2+\sqrt{10}}{8},\,\frac{\sqrt2+\sqrt{10}}{8},\,\frac{\sqrt2+\sqrt{10}}{8},\,\frac{5\sqrt2+\sqrt{10}}{8}\right).$$

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Rhombic disphenoid (720): Snub bitetrahedral diacositetracontachoron