Snub bitetrahedral tetracontoctachoron

The snub bitetrahedral tetracontoctachoron or sebtic is a convex isogonal polychoron that consists of 48 snub tetrahedra, 192 triangular antipodiums and 288 phyllic disphenoids. 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:
 * ($\sqrt{2-√2}$/4, $\sqrt{2+√2}$/4, $\sqrt{4+√10+4√2}$/4, $\sqrt{12+8√2+√266+188√2}$/4),
 * ($\sqrt{8-2√2-2√14-8√2}$/8, $\sqrt{16+6√2+2√46+32√2}$/8, $\sqrt{24+10√2+2√158+104√2}$/8, $\sqrt{32+18√2+6√46+32√2}$/8),
 * ($\sqrt{8-2√2+2√14-8√2}$/8, $\sqrt{16-2√2+2√62-16√2}$/8, $\sqrt{16+10√2+2√46+32√2}$/8, $\sqrt{40+26√2+2√670+472√2}$/8).

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:
 * ($\sqrt{2-√2}$/4, $\sqrt{2+√2}$/4, $\sqrt{6+2√2+√26+16√2}$/4, $\sqrt{26+18√2+√826+584√2}$/4),
 * ($\sqrt{12+2√2-2√14-4√2}$/8, $\sqrt{20+10√2+2√142+100√2}$/8, $\sqrt{52+30√2+2√478+332√2}$/8, $\sqrt{60+38√2+6√142+100√2}$/8),
 * ($\sqrt{12+2√2+2√14-4√2}$/8, $\sqrt{20+2√2+2√94+20√2}$/8, $\sqrt{44+30√2+2√142+100√2}$/8, $\sqrt{68+46√2+2√2078+1468√2}$/8).