# Duotruncatoprism

A **duotruncatoprism** is an isogonal polytope formed from the convex hull of two orthogonal duoprisms where one base is a truncated version of the other, forming two orthogonal rings of n 2n-gonal prisms. They are closely related to the duoexpandoprisms, differing only in the prisms and the number of rings. The simplest possible duoexpandoprism is the digonal-square prismantiprismoid, which can be thought of as a digonal duotruncatoprism, while the simplest unique duoexpandoprism is the triangular duotruncatoprism, which is the convex hull of two orthogonal triangular-ditrigonal duoprisms. The dual of a duotruncatoprism is a duotruncatotegum.

Unlike the duoexpandoprisms, which have the expanded hypercube as its only uniform solution, there are no uniform duotruncatoprisms, and they cannot be optimized either with the exception of the digonal-square prismantiprismoid, because it necessarily has a variant that approaches the minimal value but never reaches it within its topology.

The 4D duotruncatoprisms have 2 rings of 2n-gonal prisms, connected by a layer of tetragonal disphenoids, wedges, and rectangular trapezoprisms similar to that found in the duoexpandoprisms. Their vertex figures are variations of a polyhedron formed by augmenting pyramids onto two faces of a tetrahedron. If *n* is equal to 2, then the prisms become rectangles and the vertex figure becomes a mirror-symmetric notch. Analogs in higher dimensions also exist.