Gyrochoron

A gyrochoron, also known as a step tegum, is an isochoric polychoron formed as the dual to the step prism. It can have any number of cells as long as it is more than or equal to 5, while still remaining isochoric. The cell of a gyrochoron always contains two-fold rotational symmetry, and all of its faces contain mirror symmetry. The only possible vertex figures for gyrochora are trapezohedra, tetragonal disphenoids, rhombic disphenoids, and phyllic disphenoids, which are related to the possible cell types of step prisms.

Like the dual step prisms, some gyrochora can be swirlchora based on dihedra.

There exist gyrochora with any amount of cells starting from five, often more than one. This is in stark contrast to 3D space, where all isohedral shapes must have evenly many sides, and where bipyramids and trapezohedra are often the only examples of an isohedral polyhedron with a given cell count.