Bitetrahedral tetracontoctachoron

The bitetrahedral tetracontoctachoron or bitac is a convex isogonal polychoron that consists of 48 tetrahedra, 144 rhombic disphenoids, 192 triangular pyramids, 288 phyllic disphenoids, and 576 irregular tetrahedra. 1 tetrahedron, 3 rhombic disphenoids, 4 triangular pyramids, 6 phyllic disphenoids, and 12 irregular tetrahedra join at each vertex. However, it cannot be made uniform.

It can be formed as the convex hull of 2 oppositely oriented snub icositetrachora, such that the icosahedra of one snub icositetrachoron align with the tetrahedra of the other.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{3+\sqrt2}{2}}$$ ≈ 1:1.48563.

Vertex coordinates
Vertex coordinates for a bitetrahedral tetracontoctachoron, created from the vertices of a snub disicositetrachoron of edge length 1, are given by all even permutations of: as well as all permutations and even sign changes of: as well as all permutations and odd sign changes of:
 * $$\left(0,\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\sqrt{\frac{9+4\sqrt5}{8}}\right),$$
 * $$\left(\frac{\sqrt{3-\sqrt5}}{4},\,\frac{\sqrt{7+3\sqrt5}}{4},\,\frac{\sqrt{7+3\sqrt5}}{4},\,\frac{\sqrt{7+3\sqrt5}}{4}\right),$$
 * $$\left(\frac{\sqrt{3+\sqrt5}}{4},\,\frac{\sqrt{3+\sqrt5}}{4},\,\frac{\sqrt{3+\sqrt5}}{4},\,\frac{\sqrt{15+5\sqrt5}}{4}\right).$$

Another set of coordinates for a bitetrahedral tetracontoctachoron, using the ratio method to minimize edge length differences, are given by all even permutations of: as well as all permutations and even sign changes of: as well as all permutations and odd sign changes of:
 * $$\left(0,\,±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac{2+\sqrt2}{2}\right),$$
 * $$\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{4+3\sqrt2}{4}\right),$$
 * $$\left(\frac12,\,\frac{1+\sqrt2}{2},\,\frac{1+\sqrt2}{2},\,\frac{1+\sqrt2}{2}\right),$$
 * $$\left(\frac{2+\sqrt2}{4},\,\frac{2+\sqrt2}{4},\,\frac{2+\sqrt2}{4},\,\frac{2+3\sqrt2}{4}\right).$$