Birectified hecatonicosihexapentacosiheptacontahexaexon

The birectified hecatonicosihexapentacosiheptacontahexaexon, or branq, also called the birectified 321 polytope, is a convex uniform polyexon. It has 56 rectified icosiheptaheptacontadipeta, 126 birectified hexacontatetrapeta, and 576 birectified heptapeta. 3 rectified icosiheptaheptacontadipeta, 5 birectified hexacontatetrapeta, and 5 birectified heptapeta join at each triangular-rectified pentachoric duoprismatic vertex. As the name suggests, it is the birectification of the hecatonicosihexapentacosiheptacontahexaexon.

A birectified hecatonicosihexapentacosiheptacontahexaexon contains the vertices and edges of a small prismated hexacontatetrapetal prism, a terirhombated octaexon, a triangular-prismatotruncated hexateral duoprism, a hexagonal-cellirhombated dodecateral duoprism, a cubic-rectified icositetrachoric duoprism, and a cuboctahedral-truncated octahedral duoprismatic prism.