Snub hexacosihecatonicosachoron

The snub hexacosihecatonicosachoron, omnisnub hecatonicosachoron, omnisnub hexacosichoron, or snixhi is a convex isogonal polychoron that consists of 120 snub dodecahedra, 600 snub tetrahedra, 720 pentagonal gyroprisms, 1200 triangular gyroprisms, and 7200 irregular tetrahedra. Each vertex joins 4 tetrahedra and 1 of each of the other 4 cell types. It can be obtained through the process of alternating the great disprismatohexacosihecatonicosachoron. However, it cannot be made uniform, as it generally as 6 edge lengths, which can be minimized to no fewer than 3 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is approximately $$1.2661327136794291861309032$$.