The great hexacosihecatonicosihecatonicosachoron, or gixhihy, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, and 120 great dodecicosidodecahedra. 1 tetrahedron, 1 great stellated dodecahedron, and 3 great dodecicosidodecahedra join at each vertex.
The vertices of a great hexacosihecatonicosihecatonicosachoron of edge length 1 are all permutations of:
along with the even permutations of:
The great hexacosihecatonicosihecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the quasidisprismatohexacosihecatonicosachoron, diprismatohecatonicosachoron, great hecatonicosafaceted prismatohecatonicosihexacosichoron, great hexacosifaceted prismatodishecatonicosachoron, great spinoprismatohexacosihecatonicosachoron, and great spinoprismatodishecatonicosachoron.