Snub bitetrahedral tetracontoctachoron

The snub bitetrahedral tetracontoctachoron or sebtic is a convex isogonal polychoron that consists of 48 snub tetrahedra, 192 chiral triangular antipodiumss and 288 phyllic disphenoids. 2 snub tetrahedra, 4 triangular antipodiums, and 4 phyllic disphenoids join at each vertex. 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 snub bitetrahedral tetracontoctachoron, assuming that the edge length differences are minimized, are given by all even permutations with an even number of sign changes of: as well as all even permutations with an odd number of sign changes of:
 * $$\left(\frac{\sqrt{2-\sqrt2}}{4},\,\frac{\sqrt{2+\sqrt2}}{4},\,\frac{\sqrt{4+\sqrt{10+4\sqrt2}}}{4},\,\frac{\sqrt{12+8\sqrt2+\sqrt{266+188\sqrt2}}}{4}\right),$$
 * $$\left(\frac{\sqrt{8-2\sqrt2-2\sqrt{14-8\sqrt2}}}{8},\,\frac{\sqrt{16+6\sqrt2+2\sqrt{46+32\sqrt2}}}{8},\,\frac{\sqrt{24+10\sqrt2+2\sqrt{158+104\sqrt2}}}{8},\,\frac{\sqrt{32+18\sqrt2+6\sqrt{46+32\sqrt2}}}{8}\right),$$
 * $$\left(\frac{\sqrt{8-2\sqrt2+2\sqrt{14-8\sqrt2}}}{8},\,\frac{\sqrt{16-2\sqrt2+2\sqrt{62-16\sqrt2}}}{8},\,\frac{\sqrt{16+10\sqrt2+2\sqrt{46+32\sqrt2}}}{8},\,\frac{\sqrt{40+26\sqrt2+2\sqrt{670+472\sqrt2}}}{8}\right).$$

Another set of coordinates for a snub bitetrahedral tetracontoctachoron, assuming that the ratio method is used, are given by all even permutations with an even number of sign changes of: as well as all even permutations with an odd number of sign changes of:
 * $$\left(\frac{\sqrt{2-\sqrt2}}{4},\,\frac{\sqrt{2+\sqrt2}}{4},\,\frac{\sqrt{6+2\sqrt2+\sqrt{26+16\sqrt2}}}{4},\,\frac{\sqrt{26+18\sqrt2+\sqrt{826+584\sqrt2}}}{4}\right),$$
 * $$\left(\frac{\sqrt{12+2\sqrt2-2\sqrt{14-4\sqrt2}}}{8},\,\frac{\sqrt{20+10\sqrt2+2\sqrt{142+100\sqrt2}}}{8},\,\frac{\sqrt{52+30\sqrt2+2\sqrt{478+332\sqrt2}}}{8},\,\frac{\sqrt{60+38\sqrt2+6\sqrt{142+100\sqrt2}}}{8}\right),$$
 * $$\left(\frac{\sqrt{12+2\sqrt2+2\sqrt{14-4\sqrt2}}}{8},\,\frac{\sqrt{20+2\sqrt2+2\sqrt{94+20\sqrt2}}}{8},\,\frac{\sqrt{44+30\sqrt2+2\sqrt{142+100\sqrt2}}}{8},\,\frac{\sqrt{68+46\sqrt2+2\sqrt{2078+1468\sqrt2}}}{8}\right).$$