Pentacontahexahecatonicosihexapentacosiheptacontahexaexon

The pentacontahexahecatonicosihexapentacosiheptacontahexaexon, or lanq, also called the rectified pentacontahexahecatonicosahexaexon or rectified 132 polytope, is a convex uniform polyexon. It has 56 rectified pentacontatetrapeta, 126 birectified hexeracts, and 576 birectified heptapeta. 4 rectified pentacontatetrapeta, 3 birectified hexeracts, and 2 birectified heptapeta join at each triangular-tetrahedral duoprismatic prismatic vertex. It is the rectified pentacontahexahecatonicosihexaexon, the birectified pentacontahexapentacosiheptacontahexaexon, and the trirectified hecatonicosihexapentacosiheptacontahexaexon. It can therefore be considered in some ways to be a hybrid of the 3 main polytopes of E7 symmetry.

A Pentacontahexahecatonicosihexapentacosiheptacontahexaexon contains the vertices and edges of a peticellirhombated hexadecaexon, a cellirhombated demihexeractic prism, and a hexagonal-celliprismatotruncated dodecateral duoprism.