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. However, it cannot be made uniform.

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 and all sign changes of: as well as all permutations and even sign changes of: as well as all permutations and odd sign changes of:
 * (0, 1/2, (1+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/4),
 * ($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{18+8√5}$/4),
 * ($\sqrt{3-√5}$/4, $\sqrt{7+3√5}$/4, $\sqrt{7+3√5}$/4, $\sqrt{7+3√5}$/4),
 * ($\sqrt{3+√5}$/4, $\sqrt{3+√5}$/4, $\sqrt{3+√5}$/4, $\sqrt{15+5√5}$/4).

Another set of coordinates for a bitetrahedral tetracontoctachoron, using the ratio method, are given by all even permutations and all sign changes of: as well as all permutations and even sign changes of: as well as all permutations and odd sign changes of:
 * (0, 1/2, (1+$\sqrt{2}$)/2, (2+$\sqrt{2}$)/2),
 * ($\sqrt{2}$/4, $\sqrt{2}$/4, $\sqrt{2}$/4, (4+3$\sqrt{2}$)/4),
 * (1/2, (1+$\sqrt{2}$)/2, (1+$\sqrt{2}$)/2, (1+$\sqrt{2}$)/2),
 * ((2+$\sqrt{2}$)/4, (2+$\sqrt{2}$)/4, (2+$\sqrt{2}$)/4, (2+3$\sqrt{2}$)/4).